SECTION 2.4 An Introduction to Applications of Linear Equations^109
OBJECTIVE 3 Solve problems involving sums of quantities.
To solve problems involving sums of quantities, choose a variable to represent
one of the unknowns. Then represent the other quantity in terms of the same
variable.(See Example 11in Section 2.3.)
PROBLEM-SOLVING HINT
NOW TRY
EXERCISE 2
In the 2006 Winter Olympics
in Torino, Italy, Russia won 7
fewer medals than Germany.
The two countries won a total
of 51 medals. How many
medals did each country win?
(Source:U.S. Olympic
Committee.)
Finding Numbers of Olympic MedalsIn the 2006 Winter Olympics in Torino, Italy, the
United States won 11 more medals than Sweden.
The two countries won a total of 39 medals. How
many medals did each country win? (Source:U.S.
Olympic Committee.)
Step 1 Readthe problem carefully. We are given
information about the total number of
medals and asked to find the number
each country won.
Step 2 Assign a variable.
Let the number of medals
Sweden won.
Then the number of medals
the United States won.
Step 3 Write an equation.
The the number of the number of medals
total is medals Sweden won plus the United States won.39 x
Step 4 Solve the equation.
Combine like terms.
Subtract 11.
Combine like terms.Divide by 2.Step 5 State the answer.The variable xrepresents the number of medals Sweden
won, so Sweden won 14 medals. The number of medals the United States
won is
Step 6 Check.Since the United States won 25 medals and Sweden won 14, the
total number of medals was Because the
United States won 11 more medals than Sweden. This information agrees
with what is given in the problem, so the answer checks. NOW TRY
25 + 14 =39. 25 - 14 =11,
x+ 11 = 14 + 11 = 25.
14 =x, or x= 14
28
2
=
2 x
2
28 = 2 x
39 - 11 = 2 x+ 11 - 11
39 = 2 x+ 11
= + 1 x+ 112
x+ 11 =
x=
EXAMPLE 2
NOW TRY ANSWER
- Germany: 29 medals;
Russia: 22 medals