Basic Mathematics for College Students

676 Chapter 8 An Introduction to Algebra

EXAMPLE (^1) Systems Analysis A
company’s telephone use would have to increase
by 350 calls per hour before the system would
reach the maximum capacity of 1,500 calls per
hour. Currently, how many calls are being made
each hour on the system?
Analyze

• If the number of calls increases by
  350, the system will reach capacity. Given


• The maximum capacity of the
  system is 1,500 calls per hour. Given


• How many calls are currently
  being made each hour? Find

Caution! Unlike an arithmetic approach, you do nothave to determine

whether to add, subtract, multiply, or divide at this stage. Simply translate the

words of the problem to mathematical symbols to form an equation that

describes the situation. Then solve the equation.

Form

Let nthe number of calls currently being made each hour. To form an equation

involving n,we look for a key word or phrase in the problem.

Key phrase:increase by 350 Translation:addition

The key phrase tells us to add 350 to the current number of calls to obtain an

expression for the maximum capacity of the system. Now we translate the words of

the problem into an equation.

equals

n  350  1,500

Solve

We need to isolate non the left side.

To isolate n,subtract 350 from both

sides to undo the addition of 350.

Do the subtraction.

State

Currently, 1,150 calls per hour are being made.

Check

If the number of calls currently being made each hour is 1,150, and we increase that

number by 350, we should obtain the maximum capacity of the system.

This is the maximum capacity.

The result, 1,150, checks.

Caution! Always check the result in the original wording of the problem, not

by substituting it into the equation. Why? The equation may have been solved

correctly, but the danger is that you may have formed it incorrectly.



1,150

 350

1,500

n1,150

n 350  350 1,500 350

n 350 1,500

the maximum capacity

of the system.

350

increased

by

The current number

of calls per hour

Self Check 1

APARTMENT BUILDINGSOwners of

a newly constructed apartment

building would have to sell 34

more units before all of the 510

units were sold. How many of the

apartment units have been sold

to date?

Now TryProblem 19

1,5

4

0

10

0

 350

1,150

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