Basic Mathematics for College Students

1.6 Problem Solving 75

SECTION 1.6 STUDY SET

VOCABULARY

Fill in the blanks.

1. A is a careful plan or method.


2. To solve application problems, which are usually given
   in words, we those words into numbers and
   mathematical symbols.

Tell whether addition, subtraction, multiplication, or division is

indicated by each of the following words and phrases.

3. reduced 4.equal-size groups


4. triple 6.fall


5. gained 8.repeated addition

Self Check 6

BUS SERVICE Thirty-four people

were riding on bus number 481.

At 11:45 AM, it arrived at the

103rd Street stop where 6 people

got off and 18 people paid the

fare to board. As the driver

pulled away from the stop at

11:47 AM, how many riders were

on the bus?

Now TryProblem 27

75¢

people were riding on a bus on Route 66. It arrived at the 7th Street
stop at 5:30 PM, where 11 people paid the $1.50 fare to board after 16 riders had
exited. As the driver pulled away from that stop at 5:32 PM, how many riders were
on the bus?

If we carefully reread the problem, we see that the phrase to boardindicates
addition and the word exitedindicates subtraction.

Form We translate the words of the problem to numbers and symbols.

plus minus

47 11 16

SolveWe will solve the problem in horizontal form. Recall from Section 1.3 that
the operations of addition and subtraction must be performed as they occur, from
left to right.

Working left to right, do the addition

first:

Now do the subtraction.

StateThere were 42 riders on the bus after the 7th Street stop.

CheckThe addition can be checked with estimation. To check the subtraction,
use:Differencesubtrahendminuend.

 42

47  11 58.

47  11  16  58  16

  

The number

of riders on

the bus after

the stop

the number

of riders

that exited.

the number

of riders

that boarded

the number

of riders on

the bus before

the stop

is

equal

to

The number

of riders on

the bus after

the stop

Forty-seven

47

Caution! As you read a problem, it is easy to miss numbers that are written

in words. It is helpful to circle those words and write the corresponding

number above.

1.It will cost $11,390 to purchase 85 sets of bed linens. 2.There are 90 calories in a glass

of lowfat milk. 3.It will take the drilling rig 34 hours to drill 578 feet. 4.There are

206 bones in the human skeleton. 5.In a 3-gallon bottle of water, there are 48 8-ounce

servings. 6.There were 46 riders when the bus left the 103rd Street stop.

ANSWERS TO SELF CHECKS

58

 16

42

47

 11

58