Concepts
1. Applications Involving Multiple Operations 2. Computing a Mean
(Average)
Answer 1. $115 per month
TIP: The solution to Example 1 can be checked by multiplication.
Forty-eight payments of $330 each amount to 48($330) = $15,840.
This added to the down payment totals $18,340 as desired.
1. Applications Involving Multiple Operations
Sometimes more than one operation is needed to solve an application problem.
Solving a Consumer Application
Jorge bought a car for $18,340. He paid $2500 down and then paid the rest in equal monthly payments over a 4-year period. Find the amount of Jorge’s monthly payment (not including interest).
Solution:
Familiarize and draw a picture.
Given: total price: $18,340 down payment: $2500 payment plan: 4 years (48 months)
Find: monthly payment Example 1
$18,340 Original cost of car
$15,840 Amount to be paid off Minus down payment
−2,500
Divide payments over 4 years (48 months)
Operations:
1. The amount of the loan to be paid off is equal to the original cost of the car minus the down payment. We use subtraction:
$18,340 − 2,500 __
$15,840
2. This money is distributed in equal payments over a 4-year period. Because there are 12 months in 1 year, there are 4 ⋅ 12 = 48 months in a 4-year period.
To distribute $15,840 among 48 equal payments, we divide.
330 48 15,840 __
⟌ −144 _ 144
−144 _ 00
Jorge’s monthly payments will be $330.
Skill Practice
1. Danielle buys a new entertainment center with a new television for $1680. She pays $300 down, and the rest is paid off in equal monthly payments for 1 year. Find Danielle’s monthly payment.
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Solving a Travel Application
Linda must drive from Clayton to Oakley. She can travel directly from Clayton to Oakley on a mountain road, but will only average 40 mph. On the route through Pearson, she travels on highways and can average 60 mph. Which route will take less time?
95 mi
85 mi
Clayton Pearson
Oakley
120 mi
Solution:
Read and familiarize: A map is presented in the problem.
Given: The distance for each route and the speed traveled along each route
Find: Find the time required for each route. Then compare the times to determine which will take less time.
Operations:
1. First note that the total distance of the route through Pearson is found by using addition.
85 mi + 95 mi = 180 mi
2. The speed of the vehicle gives us the distance traveled per hour. Therefore, the time of travel equals the total distance divided by the speed.
From Clayton to Oakley through the mountains, we divide 120 mi by 40-mph increments to determine the number of hours.
Clayton Oakley
40 mi in 1 hr 40 mi
in 1 hr 40 mi
in 1 hr
120 mi
Time = 120 mi _______40 mph = 3 hr
From Clayton to Oakley through Pearson, we divide 180 mi by 60-mph increments to determine the number of hours.
Clayton Oakley
60 mi in 1 hr 60 mi
in 1 hr 60 mi
in 1 hr
180 mi Pearson
Time = 180 mi _______60 mph = 3 hr Therefore, each route takes the same amount of time, 3 hr.
Skill Practice
2. Taylor makes $18 per hour for the first 40 hr worked each week. His overtime rate is $27 per hour for hours exceeding the normal 40-hr workweek. If his total salary for one week is $963, determine the number of hours of overtime worked.
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Example 2
Answer
Solving a Construction Application
A rancher must fence the corral shown in Figure 1-9. However, no fencing is required on the side adjacent to the barn. If fencing costs $4 per foot, what is the total cost?
275 ft
475 ft 300 ft 200 ft200 ft
Barn
Figure 1-9 Solution:
Read and familiarize: A figure is provided.
Strategy
With some application problems, it helps to work backward from your final goal. In this case, our final goal is to find the total cost. However, to find the total cost, we must first find the total distance to be fenced. To find the total distance, we add the lengths of the sides that are being fenced.
2 1 7 15 ft
200 ft 200 ft 475 ft + 300 ft __
1450 ft
Therefore,
( Total cost of fencing ) =
( total distance
in feet ) ( cost per foot ) =
( 1450 ft ) ( $4 per ft )
=
$5800
The total cost of fencing is $5800.
Skill Practice
3. Alain wants to put molding around the base of the room shown in the figure. No molding is needed where the door, closet, and bathroom are located.
Find the total cost if molding is $2 per foot.
Example 3
Bathroom 3 ft Door3 ft
Closet 8 ft 20 ft
18 ft
2. Computing a Mean (Average)
The order of operations must be used when we compute an average. The technical term for the average of a list of numbers is the mean of the numbers. To find the mean of a set of numbers, first compute the sum of the values. Then divide the sum by the number of values. This is represented by the formula
Mean = sum of the values _______________
number of values Answer
3. $124