9.1 and 9.2 word problems9.1 and 9.2 word problems

Solving these word Solving these word problems…problems…

Set up a system of equationsSet up a system of equations Solve the system using elimination or Solve the system using elimination or

substitutionsubstitution Answer the question!!!Answer the question!!!

Example 1Example 1

A total of $12,000 is invested in two A total of $12,000 is invested in two funds paying 5% and 3% simple funds paying 5% and 3% simple interest. The yearly interest is $500. interest. The yearly interest is $500. How much is invested at each rate??How much is invested at each rate??

Example 1Example 1

Verbal modelVerbal model

5% fund + 3% fund = Total 5% fund + 3% fund = Total InvestmentInvestment

5% int. + 3% int. = Total Interest5% int. + 3% int. = Total Interest

Example 2Example 2 A shoe company invests $300,000 in A shoe company invests $300,000 in

equipment to produce a new line of equipment to produce a new line of athletic footwear. Each pair of shoes athletic footwear. Each pair of shoes costs $5 to produce and is sold for costs $5 to produce and is sold for $60. How many pairs of shows must $60. How many pairs of shows must be sold before the business breaks be sold before the business breaks even?even?

Verbal ModelVerbal Model

Total Cost = Cost x Number + Total Cost = Cost x Number + InitialInitial

per unit of unitsper unit of units cost cost Total Revenue = Price per unit x Total Revenue = Price per unit x

number number of unitsof units

Example 3Example 3 The weekly ticket sales for anew comedy The weekly ticket sales for anew comedy

movie decreased each week. At the same movie decreased each week. At the same time, the weekly ticket sales for a new time, the weekly ticket sales for a new drama movie increased each week. Models drama movie increased each week. Models that approximate the weekly ticket sales S that approximate the weekly ticket sales S (in million dollars) for each movie are(in million dollars) for each movie are

S = 60 – 8xS = 60 – 8x

S = 10 + 4.5xS = 10 + 4.5x

Where x represents the number of weeks each Where x represents the number of weeks each is in the theater. After how many weeks will is in the theater. After how many weeks will the ticket sales for the two movies be equal?the ticket sales for the two movies be equal?

Example 4Example 4

An airplane flying into a headwind An airplane flying into a headwind travels 2000 – mile flying distance travels 2000 – mile flying distance between Chicopee, Massachusetts and between Chicopee, Massachusetts and Salt Lake City, Utah in 4 hours and 24 Salt Lake City, Utah in 4 hours and 24 minutes. On the return flight, the same minutes. On the return flight, the same distance was travelled in 4 hrs. Find distance was travelled in 4 hrs. Find the airspeed of the plane and the speed the airspeed of the plane and the speed of the wind assuming both remain of the wind assuming both remain constant.constant.

Example 4Example 4

Verbal Model – Verbal Model –

Use distance = rate x timeUse distance = rate x time

Where the rate is…Where the rate is…

r1 – r2 = speed of plane against the r1 – r2 = speed of plane against the windwind

r1 + r2 = speed of plane with the windr1 + r2 = speed of plane with the wind

Example 5Example 5

The admission fee at a small fair is The admission fee at a small fair is $1.50 per child and $4.00 for adults. $1.50 per child and $4.00 for adults. On a certain day, 2,200 people enter On a certain day, 2,200 people enter the fair and $5,050 is collected. How the fair and $5,050 is collected. How many adults and children attended?many adults and children attended?

Example 5Example 5

Verbal ModelVerbal Model

let x = # kidslet x = # kids

let y = #adultslet y = #adults

# kids + # adults = total attended# kids + # adults = total attended

Price kids + price adults = total $ Price kids + price adults = total $ collectedcollected

HwHw

Pg 666 # 64, 65, 67Pg 666 # 64, 65, 67

pg 678 #43, 50, 53-55pg 678 #43, 50, 53-55