msstallions.weebly.com€¦ · web viewhow many hours if the distance travelled is 300 miles. 4....

Core II Practice 2.1 Name_________________________________ Date___________

Mike’s Mowing charges $18.00 per hour to mow lawns. Write an equation that relates cost c to hours h. Use your equation to find the cost of a four hour lawn mowing job. Use your equation to find how many hours a $72.00 job took.

1. equation

2. cost

3. hours

The distance travelled d is proportional to the number of hours h travelled at a constant rate r. Write an equation that relates distance d to hours h if the rate r is 40 mph. Use your equation to find the distance if the time travelling is 6 hours. How many hours if the distance travelled is 300 miles.

4. equation

5. distance

6. hours

To make Halloween punch a recipe calls for 4 parts lime juice mixed with 2 parts red strawberry juice. Write an equation that relates 1 lime juice l to red juice r and an equation that relates 1 red juice r to lime juice l.

7. r = _______8. l = _______9. If there are 12 parts lime juice how many parts red strawberry?

10. If there are 5 parts red strawberry how many parts lime juice?

The total cost c for ski rental is proportional to the number of days d and the daily price p. Write an equation that relates the total cost c to the number of days d and a daily price of $14.50.

11. equation

12. What is the total price for 8 days?

13. How many days rental if the cost is $43.50?

14. Write an equation that relates the total cost c to the number of days d and any daily price p.

The table shows the number of pages read n compared to the minutes spent reading m.n 3 6 9 12 15m 1 2 3 4 5

15. Find k the number of pages read each minute.

16. Use your answer from problem 15 to write an equation that relates the total number of pages t to the minutes reading m and the pages each minute k.

17. How many minutes to read 90 pages? How many hours?

18. At the rate found, how many pages are read in 2 hours?

At a school carnival experts discovered that for a successful cake auction 5 chocolate cakes are needed for every 2 white cakes.

19. Write an equation that relates one chocolate cake c to white cakes w.

20. Write an equation that relates one white cake w to chocolate cakes c.

21. If there are 15 chocolate cakes how many white cakes?

22. If there are 18 white cakes how many chocolate cakes?

23. Write a scenario for the equation d = 3.5p if d is the number of dogs.

Core II Practice 2.2 Name_______________________ Date__________

Understanding Graphs of Proportions

1. The Light Rail Line in New Jersey charges passengers for one way rides. Use the graph below to determine the charge per ride.

2. Paula babysits and charges per child. Use the graph to determine how much she earns per child.

3. Bob drives to work each day. His gas mileage is shown in the graph. What is the unit rate? What does it represent?

4. The graph shows the cost for bus fares use it to determine the charge per ride.

5. Yasmine gets paid for every dog that she walks according to the graph at the right. What does she earn per dog?

6. The carousel at the carnival is the most popular ride. The ticket taker keeps track of how many people ride during the day. Use the graph to determine how many people ride every hour.

Core II Practice 2.2a Name___________________Date ____________

Core II Practice 2.3 Name____________________________ Date________Classwork

1. Name a point using coordinate pairs.

2. Use your point to find the unit rate.

3. Explain what your point (x, y) means in context of the situation.

4. Write the unit rate as a coordinate pair (1, r).

5. Draw in the “stairsteps” to indicate slope. Name the slope in simple form.

6. Compare the slope and the unit rate.



















25. What are some differences and similarities between the last graph and the first three graphs?

Core II Practice 2.4 Name______________________________ Date_____

Use the formula I = prt to answer the following. I is interest earned at the rate r (written as a decimal) for t time in years. p is principal which is the amount of money at the beginning.

1. Billy has $400.00 which he plans on investing at 5% for the next five years. What will his investment earn?

2. Suzy borrowed 1249.89 at 4.5% simple interest for 2 years. How much is the interest?

3. Ellie May put 575.00 in a simple interest account @ 7.5% for 6 years. What is the total amount of the account including interest at the end of the 6 years

4. Jethro won $30,000.00 and invested his money at 4.25% simple interest for 412 years. How much

did his $30,000.00 earn?

5. After a big payday Ringo placed $1450.69 in an account @ 7.5% for 18 months. What amount of interest did his investment earn?

6. Jack and Jill each received gifts of $1200 each. Jack placed his money in an investment for 3 years

at 5.5% simple interest. Jill invested her money for 512 years at 3% interest. Who made the most on

their investment? Defend your answer by showing your work.

7. Explain what it means when a person says, “My investment made 5% simple interest for three years.”

Core II Practice 2.5 Name________________________ Date____________

Three Types of Percent Problems

Solve each problem using the percent proportion: %100

= partwhole .

1. What is 94% of 44?

2. 40% of 151 is what amount?

3. Find 360% of 60.

4. What is 84% of 65?

5. Find 190% of 95.

6. 95 is 34% of what number?

7. 5% of what is 95.5?

8. 106 is 15% of what?

9. 24 is 120% of what amount?

10. 85.2 is 24% of what?

11. 11 is what percent of 150?

12. 18 is what percent of 15?

13. What percent of 68 is 32.1?

14. What percent of 93 is 22?

15. 92.2 is what percent of 156?

16. 18 of the 90 kids at the carnival were seventh graders. What percent were seventh graders?

17. 15% of $128.59 is how much money?

18. 6% of the $459.50 price is how much sales tax?

19. 6% of the original price is $4.50. What was the original price?

20. Of 83 kids who participate in winter sports 19 picked skiing as their favorite. What percent picked skiing?Core II Practice 2.6 Name_____________________________ Date____________

Answer each of the following:

1. 40% of 102 is what?

2. What is 190% of 117?

3. 46% of 70 is what amount?

4. What number is 37% of 91.3?

5. Find 360% of 82.

6. 111 is 98% of what?

7. 57 is 15% of what?

8. 34% of what is 47?

9. 52.5 is 120% of what amount?

10. 4.6 is 59% of what number?

For problems 11-15 write a “universal percent” type question. (Percent of whole is what part?)

11. Write a simple word problem for the following proportion: %100

=3958

12. Write a simple word problem for the following proportion: %100

=7516

13. Write a simple word problem for the following proportion: 400100

=150w


100= p

31


100= p

118.4For problems 16-20 write a “real life” scenario that fits the proportion. Solve.

16. 25100

= p80

17. %100

=1845

18. 42100

=20w

19. 60100

= p250

20. %100

=20050

Core II Practice 2.7 Name____________________________ Date____________

Sale price/sales tax Worksheet

Find the amount of sales tax or savings for each.

1. $115.00 cat discounted 15% 2. $98.00 coat with 5% sales tax

3. $45.00 book with Idaho sales tax 4. $315.89 skis reduced 20%

5. 6% sales tax on a $129.85 item 6. $229.59 puppy with 7% tax

7. $13 socks @ 25% off 8. $65.75 dinner with 6% sales tax

9. Snowboard regularly priced at $419.79 reduced 30%

10. $155.69 IPOD reduced 17%

Find the final price of each.

11. $115.00 cat discounted 15% 12. $98.00 coat with 5% sales tax

13. $45.00 book with Idaho sales tax 14. $315.89 skis reduced 20%

15. 6% sales tax on a $129.85 item 16. $229.59 puppy with 7% tax

17. $13 socks @ 25% off 18. $65.75 dinner with 6% sales tax

19. Snowboard regularly priced at $419.79 reduced 30%

20. $155.69 IPOD reduced 17%

over

Find the sale price including Idaho sales tax.

Example: $65.39 sweater reduced 15% in Idaho.Step 1. Find amount of discount d=65. 39×0 .15 d=9 .8085

Step 2. Round to the nearest cent if needed 9 .8085≈$ 9 . 81

Step 3. Find sale price

sp=65.39−9 .81sp=$ 55 .58

Step 4. Find sales tax on sale price

tax=55. 58×0 .06tax=3 .3348

Step 5. Round to nearest cent if needed 3 .3348≈$3 .33

Step 6. Add sales tax to sales price

total=55 .58+3 .33total=$58 . 91

21. $158.00 boots reduced 20%

22. $14.50 CD on sale for 33% off

23. $27.89 dinner bill with 15% savings

24. 24% reduction on a $67.59 pair of shoes

25. $95.89 skunk @ 17% off

26. Consider problem 21. Billy found the tax, added the tax to the price, then found the discount and

subtracted to find the final price. Suzy found the discount, subtracted the discount from the price, then

found the tax and added to get the final price. Whose method was correct? Explain your reasoning and

justify your answer mathematically

Core II Practice 2.8 Name______________________ Date_________

Answer the following.

1. The population of your town was 14,500 people. The latest census indicates the population has decreased by 18%. What is the current population of your town?

2. Your bill at a restaurant is $109.99. Since you are a frequent customer, the manager offers you a 15% discount. What is the amount of your discount?

3. The original price of a microscope is $274.50. If you wait for it to go on sale for 30% off, what will the sale price be?

4. You have $20 and would like to purchase a sweater that is on sale for 35% off. The original price of the sweater is $29.50. Can you afford to buy it on sale?

5. The new computer you want to buy costs $749.50. The store salesman earns 12% commission on the sale amount. How much does the salesman earn?

6. Calculate an 18% tip on a $84 bill.

7. A car costs $34,500. The car sales person earns 15% commission on the price of the car. How much commission is paid on the sale?

8. The population of your town has grown by 8% over the last year. If the population one year ago was 25,000 people what is the current population?

9. You have $70 in your purse. Your bill at a restaurant is $58. Do you have enough money to leave an 18% tip?

10. How much money do you spend on a $55 dinner with a 20% tip?

11. Calculate an 18% tip on a $47 bill

12. You upgrade your computer so that its memory capacity increases by 34%. If your old memory capacity was 18 megs, what is your new capacity?

13. How much money will do you spend on a $110 meal with 20% tip?

14. You calculated an 18% tip on your meal bill to be $24. What was the cost of your meal?

15. A television is on sale for 15% off the original price of $1,400. When it doesn’t sell, the manager marks it down another 10% off the sale price. What is the new sale price of the television?

16. After looking at your bill, you calculate an 18% tip to be $14. What was the original bill?

17. How much money will you spend if your lunch bill is $28, you pay 8% tax and you leave an 18% tip?

18. The price on a new television is $879.98. The seller earns a 15% commission on the amount of sales. What is the amount of seller’s commission?

19. The commission of 7.5% on sales for a salesperson was $120.00. What was the amount of sales?

20. The common rate for restaurant tips is 15%. A dinner bill was $129.95. What amount should the tip be?

Core II Practice 2.9 Name_____________________ Date_______

Find the percent of change. Remember to state if it is an increase or a decrease. Round your answers to the nearest tenth.

1. Original amount: 17; New amount: 23




5. You purchase a stereo for $53 then sell it on Craigs List for $26.

6. From 23 to 89

7. Your baby sister grows from 29 inches to 49 inches.

8. From 32 feet to 13 feet

9. A bridge is retrofitted and can now hold more weight. It originally held 39 tons. It can now hold 74 tons.

10. Your school went to block scheduling. Classes used to be 42 minutes long. They are now 91 minutes long.

11. You purchase a painting for $55 then sell it on Ebay for $91.

12. From 59 to 87

13. Your dog loses weight. She originally weighed 62 pounds and now she weighs 51 pounds.

14. From 65 feet to 47 feet.

15. The amount of sugar in a soft drink is decreased from 68 grams to 11 grams.

16. The amount of time allowed for a test is changed from 20 minutes to 42 minutes.

Core II Practice 2.10 Name___________________________ Date________

Find the percent of error. Round your answer to the nearest tenth of a percent.

1. A mineral sample is weighed and the mass is recorded as 175gm. Actual mass is 180gm. What is the percent of error?

2. Billy Bob hosts a barbeque at his ranch. He estimates the number of guests to be about 250. An actual count of the guests is made and Billy discovers that 225 people attended. What is the percent of error?

3. A dinner bill is $49.85. The bill is $4.00 more than expected. What is the percent of error?

4. An earthworm is measured and the length is recorded as 105mm. The actual length is known to be 110mm. What is the percent of error?

5. During a fundraiser, carnival participants are supposed to guess the number of jelly beans in a sealed jar. The closest guess wins. The carnival organizers have counted the actual amount and found there are 719 jelly beans in the jar. The winner (who won $50.00) guessed 689 jelly beans in the jar. What is the percent of error?

6. Jean Claude woke up one morning and found out that overnight 18 inches of snow had fallen. He remembered that he had estimated the snowfall and found that his estimate was incorrect by 2.5 inches. What is the percent of error?

7. Suzy Que just finished an extremely difficult math test and estimated her grade to be about 72%. After the test was graded she received an 80%. Her guess is incorrect by what percent of error?

8. The volume of soda in a bottle is labelled as 2.00 litres. Manufacturers are allowed to be over or under by 0.02 litres. What is the allowable percent of error?

9. Ringo and John project sales of their first music album to be $110,000. After exceptional sales the amount is actually $2,180,000. What is the percent of error?

10. Heidi the hiker estimates her day’s journey. After the hike she uses a GPS device to track her route and finds that the real distance of 18km was over her estimate by 1.75km. What is the percent of error?

11. Once a year a wishing well is cleaned out and the money is donated to charity. Workers decided ahead of time to guess the amount in the well. After cleaning the well, the actual amount counted was $200.00 and it is discovered that the guess was over by 10%. What was the worker’s guess?

12. A controversial jump in middle school long jumping was measured at 12ft by inexperienced officials. Expert officials remeasured the jump at exactly 150in. What is the percent of error?

13. Prior to an actual survey it was estimated that 650 people would be interested in participating in a “Middle of Winter” swim and fun run. Survey results indicate that only 53 people are interested in the event. What is the percent of error?

14. Before shopping, Betty Sue estimated her grocery bill to be about $175.00. Much to her surprise the bill was only $139.73. Her estimate was incorrect by what percent?

15. A hunter has an extremely accurate rangefinder that indicates a target is 350 yards away. A novice distance estimator guesses the distance incorrectly by guessing 20% over. What was the novice’s guess?

Core II Practice 2.11 Name________________________ Date__________Mixed up algebra equation worksheet Solve the following. SHOW WORK!!!!!

1. 6m=42 2. f8=9

3. m+15=31

4. d−29=47 5. −56 t=−4 6. d−23=−18

7. x+(−7 )=30 8. k+14=10 9. 3 s16

=−27

10. −813

=−2 x 11.

−a6=18 . 4

12. d− (−8 )=−18

13. −1

5=d+ 3

5 14. −4 .5=−0 . 05 n 15. 37=m−39

16. −21=m

8 17. 14n15

=−1625 18. m+(−25 )=−25

19. h−(−2 .56 )=−32 .8 20. m+26=−27

Write an inverse operation equation for the following. Solve.

21. Jethro has a certain amount of money in his pocket. He finds $27.00 and now has $50.00. What was the amount in his pocket?

22. A board is to be cut up into 7 pieces that are equal length. Each piece will be 4.5 feet long. How long is the original board?

23. Mrs. Jones had lots of friends on Facebook but she unfriended 17 of them. The result is 68 friends remaining. How many friends did she have originally?

24. The seventh grade ski team is 8 times as big as the sixth grade ski team. The seventh grade team has 84 members. How big is the sixth grade team?

25. The sum of a number and -48 is 109. What is the other number?

Core II Practice 2.12 Name_______________________ Date_________

Properties

1) Identify the property as Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, or Associative Property of Multiplication, or Distributive Property.

a. 3 x (4 x 5) = (3 x 4) x5

b. 6 + 5 = 5 + 6

c. 2(4x + 5) = 8x + 10

d. 2 + (9 + 4) = (2 + 9) + 4

e. r + t = t + r

f. f (gh) = (fg)h

g. xy + xz = x(y + z)

h. 12 (10 x 8) = (10 x 12) 8

i. 5(2x) = 2(5x)

j. 3 + (b + 9) = (3 + b) + 9

Combining Like Terms2) Simplify the expression if possible.

a. 7x + 8x

b. 6x + 8y + 2x

c. 15x2 + 5x2

d. -10y + 4y

e. x + 2x

f. x2 + 5x2

g. 2x + 4x + 3

h. 6y – 3y

i. 9y + 4y – 2y + y

Homework3) Simplify the expression if possible.

a. 15x2 + 5x2 + 2x

b. -10y + 4y – 5

c. x + 2x + x + 5x

d. 6x2 + 5x2

e. 12x + 14x + 3y

f. 6y – 3y + 6xy + 4xy

g. 9y + 4y – 2y + y

h. x + 5x + x + 12 – 7x

i. 8x – 3x + 2x + 15 – 7x

Answer the following:4) For a school play adult tickets were $4.00 each and student tickets were $2.00 each. The

expression 4 a+2 s gives the total amount of money taken in from ticket sales.

a. Find the amount from ticket sales.

b. From the expression what does the term 4 a mean?

c. From the expression what does the term 2 s mean?

d. How many dollars were earned from adult tickets?

e. How many dollars were earned from student tickets?

Core II Practice 2.15 Name_____________________________ Date_______1) Use the Distributive Property to factor the following expressions.

a. 5x + 35

b. 2x + 24x

c. 7r + 42t

d. 3j + 24k + 33m

e. -9p + 6q

f. -15n – 45v

g. 16y + 56z

h. 8e + 24f + 28g

i. -14r + 21t

j. -9c – 15h2) Use the Distributive Property to expand the expressions without parentheses.

a. 6(x + 4)

b. -1(x – 4)

c. (x + 2)8

d. ⅝(4x + 12)

e. 1.2(3x – 7.1)

f. 7(x – 12)

g. 3(x - 14)

h. (x - 2)5

i. ⅔(6x + 12)

j. 2.5(3x – 4.1)

3) If an equilateral triangle has a perimeter of 12w + 18, how much is each side?

4) If a square has a perimeter of 8x + 36, how much is each side?

5) If an equilateral triangle has a perimeter of 21w + 14, how much is each side?

6) If a square has a perimeter of 20x + 12, how much is each side?

7) Billy says the expression 5 x+10is equivalent to the expression5 ( x+2 ). Is Billy correct? Justify your answer.

7) Suzie claims the expression 3 (2 x+7 )−5 is equivalent to 6 x+2. Is Suzie’s claim correct? Justify your answer.

9) The perimeter of a rectangle can be found using the expression 2 l+2 w. Rewrite the expression after factoring.

Core II Practice 2.16 Name_________________________________ Date________

Write an expression for each of the following.

1. A plumber charges $27.00 per hour.

2. The cost for a taxi is $5.00 plus $2.50 per mile.

3. The perimeter of a rectangle is twice the length plus twice the width.

4. The food costs for the party will be $12.95 per pizza added to $1.79 per drink.

5. The price for each of the 7 travellers is the cost of gas divided by 7.

6. The weekend’s pay for Sally will be $9.50 times the total of her hours worked on Saturday (t) and Sunday (n).

7. Mick’s daily pay was his total pay (p) divided by the number of days he worked (d).

8. three times a number decreased by 5

9. a number decreased by 5 multiplied by three

10. The temperature increased by15.5 degrees.

11. the quotient of a number and 5

12. a number decreased by 12

13. 35 subtracted from a number

14. 6% of the price (p).

15. The price including Idaho tax will be the original price added to 6% of the price.

16. 14 of a number m.

17. the sum of a number x and another number m

18. the difference of 47 and a number p

19. the product of -16, a number k and another number f

20. a number w increased by the product of 5 and a number t

Billy works two different jobs that each pay $10.00 per hour. One job is at Happy Harps Music Store and last week he worked h number of hours. His other job is working for Superwash Car Wash and he worked s number of hours. Write two different expressions that give his total pay.

21. Expression that gives total hours then total pay.

22. Expression that gives total pay at each job then total pay.

A cell phone plan charges $19.95 service charge per month plus $0.25 per text plus $0.5 per minute of call time.

23. What is the amount of service charge?

24. What is an expression for the amount charged for texting?

25. Write an expression for the amount charged for minutes of calls.

26. Write an expression for the total monthly plan.

Core II Practice 2.17 Name________________________________ Date______

For each scenario write an expression that contains more than one term (yes they can be two or more similar terms). Rewrite the expression in simplified form or rewrite using the distributive property.

The price increased by 6%. The price reduced by 15%.1. unsimplified form 3. unsimplified form

2. simplified form 4. simplified form

The number of kids decreased by 25%. The inches of snow increased by 20%.5. unsimplified form 7. unsimplified form

6. simplified form 8. simplified form

The perimeter of a rectangle.9. expression

10. rewritten using dist. prop.

The sum of points from touchdowns (6t) from each of five games.11. expression (with several terms)

12. simplified form

The scenario for a price increased by 5% can be written p + 0.05p. This expression can be rewritten as 1.05p so that p + 0.05p = 1.05p. This means that, “p increased by 5%” is the same as “multiply p by 1.05”

13. Use “The price increased by 6%” to fill in the blanks for the following:p _______________ by 6% is the same as multiply by _______.

14. Use “The price reduced by 15%” to fill in the blanks for the following:P decreased by ________ is the same as ___________ by ____.

15. Write a similar “is the same as” statement for the following.The weight (w) increased by 30%.

Core II Practice 2.18 Name___________________________ Date_______Solve the following equations for the given variable.

1. 2 x+5=29 2. x3+5=13 3. −5 x+7=52

4. – x−17=32 5. 19=m6

−7 6. 23

r−13=5

7. −8=9 m+19 8. 45=−7 d−25 9. t

2.5+8.9=5.4

10. 32

b+ 14=2

3 11. 4.5 n+2.6=10.7 12. −9 k−28=−73

Write an equation and solve.Three times a number added to 7 is 31.12. equation

13. solution

Billy buys one $5.00 burger and three drinks for $14. How much for the drinks?14. equation

15. solution

The product of 6 and some number added to 12 is 42.16. equation

17. solution

Suzie works for $7.50 per hour and receives $29.00 in tips for one afternoon of working as a waitress. Her pay for the afternoon is $74.00. How many hours did she work?18. equation

19. solution

20. Write a scenario for the equation 6 x+13=55

Core II Practice 2.19 Name___________________ Date__________

Solve each equation.

1. 5 x+3x=32 2. m−4 m=21 3. 35=−6 m−m

4. 15 n=78+ (−3 ) 5. 18

x+ 38

x=14 6. 15−24= x2

7. t4=−13+5 8.

d−3

=42+(−34 ) 9. p+0.6 p=47.70

10. 8.5 n−2.2n=9.45 11. 8 x=2 x+42 12. −63+4n=−5n

Write an equation and solve.

Three times a number increased by the same number is 28.

13. equation

14. solution

Billy Bob works 7 hours on Monday and 9 hours on Tuesday. His total pay is $208. How much is he paid per hour?

15. equation

16. solution

The product of seven and a number is the sum of 45 and 39.

17. equation

18. solution

The price increased by 6% of the price is $74.20. What was the original price?

19. equation

20. solution

21. Write a scenario for 5 x+6 x=77

Core II Practice 2.20 Name_____________________________ Date_______Solve each equation.

1. 2 (2 x+5 )=19 2. 5 ( x−6 )=10 3. −3 (2m+5 )=27

4. −(2 x−6 )=28 5. 68=4 (5 x+2 ) 6. −44=8 (x−3 )

7. 18=−3 (−2 d−6 ) 8. 0.5 (10 x−12 )=66 9. −105=7(3 x−6)

10. 64=2(3 x−1) 11. 5 ( x+18 )=−55 12. −45=6 (2x+4)

Write an equation and solve.Four times the sum of a number and 8 is 32.13. equation

14. solution

The difference of two times number and 6, multiplied by 5 is 50.15. equation

16. solution

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