Basic Mathematics for College Students

1.6 Problem Solving 69

To solve application problems, which are usually given in words, we translate
those words to numbers and mathematical symbols. The following table is a
review of some of the key words, phrases, and concepts that were introduced in
Sections 1.2-1.5.

Addition Subtraction Multiplication Division Equals

more than how much more double distributed equally same value

increase less than twice shared equally results in

gained decrease triple split equally are

rise loss of per is

total fall times among was

in all fewer at this rate goes into yields

forward reduce repeated addition equal-sized groups amounts to

altogether decline rectangular array how many does each the same as

EXAMPLE (^1) Table Settings One
place setting like that shown on the right costs
$94. What is the total cost to purchase these
place settings for a restaurant that seats 115
people?
AnalyzeAt this stage, it is helpful to list the
given facts and what you are to find.

• One place setting costs $94. Given


• 115 place settings will be
  purchased. Given


• What is the total cost to
  purchase 115 place settings? Find

Form The key word totalsuggests addition. In this case, the total cost to purchase
the place settings is the sum of one hundred fifteen 94’s. This repeated addition can
be calculated more simply by multiplication.
We translate the words of the problem to numbers and symbols.

is equal to times

The total cost 115 $94

of the purchase

 

the cost of one

place setting.

the number of place

settings purchased

The total cost

of the purchase

Self Check 1

BEDDING One set of bed linens

costs $134. What is the total cost

to purchase linens for an 85-bed

hotel?

Now TryProblem 17

The Language of Mathematics A strategyis a careful plan or method. For

example, a businessman might develop a new advertising strategyto increase

sales or a long distance runner might have a strategyto win a marathon.