bkevil solving percent equations using proportions proportion is two equal fractions

$: Bkevil Solving Percent Equations Using Proportions Proportion is two equal fractions$
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Solving Percent Solving Percent Equations Using Equations Using

ProportionsProportions

d

c

b

a

)(

)(

100

%

oftotal

ispart

Proportion is two equal fractions

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Percent EquationsPercent Equations

•Remember “percent” means:Remember “percent” means:• Out of 100Out of 100• Per 100Per 100• part of a total of 100part of a total of 100

100

5.82%5.82

100

30%30

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Write every problem, with a percent, in this equation form:

percent of total is part

75% x 60 = 4575%

percent x

of

60

total

=

is

45

part

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II. Total is unknown -- “X”

3 kinds of percent equations

I. Percent is unknown -- “X”

III. Part is unknown -- “X”

percent of total is part

X

X of total is part

X

percent of X is partpercent of total is X

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Write a proportion when percent is missing.

I. percent of total is part

75% x 60 = 45X %

percent

60

45

100

x

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Solve the proportion:

75% x 60 = 45X %

60

45

100

x

60 X = 100(45)

Cross multiplySolve equation

60 X = 4500 X = 75 X% =

75%

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Write a proportion when total is missing.

II. percent of total is part

75% x 60 = 45X

total

x

45

100

75

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75% x 60 = 45X

x

45

100

75

75X = 100(45)


75X = 4500 X = 60 X = 60

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Write a proportion when part is missing.

III. percent of total is part

75% x 60 = 45X

part

60100

75 x

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75% x 60 = 45X

60100

75 x

75(60) = 100(X)


4500 = 100 X X = 45 X = 45

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Remember---Remember---

• If the “If the “X” is over 100, your ” is over 100, your answer should have a answer should have a percentpercent sign “%”.sign “%”.

• If the “If the “X” is anywhere else in ” is anywhere else in the proportion, your answer the proportion, your answer should should NOTNOT have a percent have a percent sign.sign.

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Example 1– Example 1– partpart is is missingmissing

• You plan to buy a radio that costs You plan to buy a radio that costs $49.99. If the local sales tax is 7%, $49.99. If the local sales tax is 7%, how much must you add to the price how much must you add to the price of the radio?of the radio?

• Rewrite the question as a % equation:Rewrite the question as a % equation:

What is 7% of 49.99What is 7% of 49.99??• Rewrite as: Rewrite as: percent of total is partpercent of total is part

7% 7% xx 49.99 = 49.99 = X

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Example 1-cont.Example 1-cont.

Solve the proportion:7% x 49.99 = 45

X

99.49100

7 x

7 (49.99) = 100(X)


349.93 = 100 X X = 3.4993 tax=

$3.50

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Example 2-Example 2-totaltotal is is missingmissing

• A company sent out survey A company sent out survey forms to everybody in a forms to everybody in a particular area. After two weeks, particular area. After two weeks, 1450 people had returned their 1450 people had returned their survey forms. If the returned survey forms. If the returned forms represent 18% of the total forms represent 18% of the total sent out, how many surveys sent out, how many surveys were sent out?were sent out?

is

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• Rewrite the question as a % Rewrite the question as a % equation:equation:

1450 is 18% of1450 is 18% of X ??• Rewrite as:Rewrite as: percent of total is partpercent of total is part

118% 8% x x X = = 14501450•Write a proportion and solveWrite a proportion and solve

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Solve the proportion:18% x X = 45

x

1450

100

18

18 X = 100(1450)


18 X = 145000X =

8055.555 8056 surveys

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Example 3 Example 3 – – %% is missingis missing

Suppose you must work 40 Suppose you must work 40 hours each week to get your hours each week to get your full paycheck. This week, full paycheck. This week, you have worked 36 hours. you have worked 36 hours. What percent of the What percent of the requirement have you requirement have you fulfilled?fulfilled?

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• Rewrite the question as a % Rewrite the question as a % equation:equation:

36 is36 is X% of 40?% of 40?• Rewrite as:Rewrite as: percent of total is percent of total is

partpart

X % % xx 4040 = = 3636•Write a proportion and solveWrite a proportion and solve

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Solve the proportion:X % 40 = 36

40

36

100

x

40 X = 100(36)


40 X = 3600X = 90 90% fulfilled

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Simple InterestSimple Interest

• InterestInterest = Principal x Rate x Time = Principal x Rate x Time

• I = prtI = prt• PrincipalPrincipal is amount of money bowered is amount of money bowered

or invested.or invested.• RateRate is the percent. is the percent.

Amount (of cents) paid for $1. Must be Amount (of cents) paid for $1. Must be changed to a decimal. (move the changed to a decimal. (move the decimal 2 places to the left)decimal 2 places to the left)

• TimeTime must be in years!!!! must be in years!!!!

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Example 4Example 4

• You put $500 in a savings account. The You put $500 in a savings account. The account pays 4% interest. You leave the account pays 4% interest. You leave the money in the account for 6 years. How money in the account for 6 years. How much interest will you receive?much interest will you receive?

• PrincipalPrincipal is the amount of money is the amount of money invested —in this case, $500.invested —in this case, $500.

• RateRate is the percent as a decimal—in this is the percent as a decimal—in this case 4% = 0.04.case 4% = 0.04.

• TimeTime is years—in this case, 6. is years—in this case, 6.

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Example 4- cont.Example 4- cont.

InterestInterest is money paid for the is money paid for the use of money.use of money.

I = p I = p xx r r xx t t formula

I = 500 I = 500 xx .04 .04 xx 66

substitution

I = 120I = 120$120 $120 interestinterest

answer labeled

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Example 4 – cont.Example 4 – cont.

• What if you were asked “What if you were asked “How much How much money will be in the account at the money will be in the account at the end of the time period of six years?end of the time period of six years?– AddAdd the the principalprincipal (the amount you (the amount you

put in the account) and the put in the account) and the interestinterest (the amount of $ the bank added).(the amount of $ the bank added).

– In this case, add In this case, add $500$500 and and $120$120..

Principal + Interest = Principal + Interest = Total AmountTotal Amount $500 + $120 =$500 + $120 = $620 $620

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bkevil solving percent equations using proportions proportion is two equal fractions

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