Page 622 - Basic College Mathematics with Early Integers

S E C T I O N 8.5 I EQUATIONS AND PROBLEM SOLVING 599

To check, notice that the total number of miles is 963 + 2054 = 3017 miles , the
given total of miles.Also, 2054 is 1091 more miles than 963, so the solution checks.
Then, state your conclusion: The distance from Chicago to Boston is 963 miles.
Work Practice 4

Example 5 Calculating Separate Costs PRACTICE 5
A salesperson at an electronics store sold a computer A woman’s $57,000 estate is to
system and software for $2100, receiving four times as be divided so that her husband
much money for the computer system as for the soft- receives twice as much as her
ware. Find the price of each. son. How much will each
receive?
Solution:

1. UNDERSTAND the problem. We read and
reread the problem. Then we choose a variable to
represent an unknown. We use this variable to
represent any other unknown quantities.We let

x = the software price
4x = the computer system price
2. TRANSLATE the problem into an equation.
In words:
software computer
and is 2100
price price
T T T T T
Translate: x + 4x = 2100
3. SOLVE the equation:

x + 4x = 2100
5x = 2100 Combine like terms.
5x 2100
= Divide both sides by 5.
5 5
x = 420 Simplify.

4. INTERPRET the results. Check the proposed solution in the stated problem.
The software sold for $420. The computer system sold for 4x = 4($420) =
$1680. Since $420 + $1680 = $2100, the total price, and $1680 is four times
$420, the solution checks. State your conclusion:The software sold for $420, and
the computer system sold for $1680.
Work Practice 5

Answer
5. husband: $38,000; son: $19,000