Basic Mathematics for College Students

1.6 Problem Solving 73

Form In the last sentence of the problem, the phrase in allindicates addition. We
translate the words of the problem to numbers and symbols.

plus plus plus

19 23 54 2

SolveWe use vertical form to perform the addition:

StateThere are 98 musicians in the orchestra.

CheckTo check the addition, we will add upward.

The result checks.

We could also use estimation to check the result. If we front-end round each
addend, we get Since the answer, 98, and the estimate,
92, are close, the result seems reasonable.

20  20  50  2 92.

98

19

23

54

 2

98

Add

bottom

to top

1

1

9

23

54

 2

98

   

The total

number

of musicians

in the

orchestra

the

number

in the

percussion

section.

the

number

in the

string

section

the

number

in the

brass

section

the

number

in the

woodwind

section

is

equal

to

The total

number of

musicians

in the

orchestra

2 Solve problems requiring more than one operation.

Sometimes more than one operation is needed to solve a problem.

EXAMPLE (^5) Bottled Water How many 6-ounce servings are there in
a 5-gallon bottle of water? (Hint:There are 128 fluid ounces in 1 gallon.)
AnalyzeThe diagram on the next page is helpful in understanding the problem.

• Since each of the 5 gallons of water is 128 ounces, the total number of
  ounces is the sum of five 128’s. This repeated additioncan be calculated
  using multiplication.


• Since equal-sizedservings of water come from the bottle, this suggests
  division.


• Therefore, to solve this problem, we need to perform two operations:
  multiplication and division.

Self Check 5

BOTTLED WATER How many

8-ounce servings are there in a

3-gallon bottle of water? (Hint:

There are 128 fluid ounces in

1 gallon.)

Now TryProblem 25