Beginning Algebra, 11th Edition

NOTE The problem in Example 2could also be solved by letting xrepresent the

number of medals the United States won. Then would represent the number

of medals Sweden won. The equation would be different.

The solution of this equation is 25, which is the number of U.S. medals. The number

of Swedish medals would be The answers are the same,whichever

approach is used, even though the equation and its solution are different.

Finding the Number of Orders for Tea

The owner of Terry’s Coffeehouse found that on one day the number of orders for tea

was the number of orders for coffee. If the total number of orders for the two drinks

was 76, how many orders were placed for tea?

Step 1 Readthe problem. It asks for the number of orders for tea.

Step 2 Assign a variable.Because of the way the problem is stated, let the variable

represent the number of orders for coffee.

Let the number of orders for coffee.

Then the number of orders for tea.

Step 3 Write an equation.Use the fact that the total number of orders was 76.

The orders for orders

total is coffee plus for tea.

76 x

Step 4 Solve.

Multiply by

57 =x

3

4.

3

4

1762 =

3

4

a

4

3

xb

76 =

4

3

x

1

3

= + x

13 x=

x=

1

3

EXAMPLE 3

25 - 11 =14.

39 =x+ 1 x- 112

x- 11

110 CHAPTER 2 Linear Equations and Inequalities in One Variable

NOW TRY
EXERCISE 3
In one week, the owner of
Carly’s Coffeehouse found
that the number of orders for
bagels was the number of
orders for chocolate scones.
If the total number of orders
for the two items was 525,
how many orders were placed
for bagels?

2

3

Be careful!

This is not

the answer.

In Example 3,it was easier to let the variable represent the quantity that was

notspecified. This required extra work in Step 5 to find the number of orders

for tea. In some cases, this approach is easier than letting the variable represent

the quantity that we are asked to find.

PROBLEM-SOLVING HINT

Combine like terms.

x= 1 x=^33 x ;

Step 5 State the answer.In this problem, x does not represent the quantity that we

are asked to find.The number of orders for tea was So is

the number of orders for tea.

Step 6 Check.The number of orders for tea, 19, is one-third the number of orders

for coffee, 57, and Since this agrees with the information

given in the problem, the answer is correct. NOW TRY

19 + 57 =76.

1

3 1572 =^19

1

3 x.

NOW TRY ANSWER

3. 210 bagel orders

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