9.1 and 9.2 word problems

Solving these word problems… Set up a system of equations Set up a system of equations Solve the system using elimination or substitution Solve the system using elimination or substitution Answer the question!!! Answer the question!!!

Example 1 A total of $12,000 is invested in two funds paying 5% and 3% simple interest. The yearly interest is $500. How much is invested at each rate?? A total of $12,000 is invested in two funds paying 5% and 3% simple interest. The yearly interest is $500. How much is invested at each rate??

Example 1 Verbal model Verbal model 5% fund + 3% fund = Total Investment 5% int. + 3% int. = Total Interest

Example 2 A shoe company invests $300,000 in equipment to produce a new line of athletic footwear. Each pair of shoes costs $5 to produce and is sold for $60. How many pairs of shows must be sold before the business breaks even? A shoe company invests $300,000 in equipment to produce a new line of athletic footwear. Each pair of shoes costs $5 to produce and is sold for $60. How many pairs of shows must be sold before the business breaks even?

Verbal Model Total Cost = Cost x Number + Initial Total Cost = Cost x Number + Initial per unit of units cost per unit of units cost Total Revenue = Price per unit x number of units Total Revenue = Price per unit x number of units

Example 3 The weekly ticket sales for anew comedy movie decreased each week. At the same time, the weekly ticket sales for a new drama movie increased each week. Models that approximate the weekly ticket sales S (in million dollars) for each movie are The weekly ticket sales for anew comedy movie decreased each week. At the same time, the weekly ticket sales for a new drama movie increased each week. Models that approximate the weekly ticket sales S (in million dollars) for each movie are S = 60 – 8x S = x Where x represents the number of weeks each is in the theater. After how many weeks will the ticket sales for the two movies be equal?

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

Example 4 Verbal Model – Verbal Model – Use distance = rate x time Where the rate is… r1 – r2 = speed of plane against the wind r1 + r2 = speed of plane with the wind

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

Example 5 Verbal Model Verbal Model let x = # kids let y = #adults # kids + # adults = total attended Price kids + price adults = total $ collected

Hw Pg 666 # 64, 65, 67 Pg 666 # 64, 65, 67 pg 678 #43, 50, 53-55