SECTION 2.3 Applications of Linear Equations 75
11.The product of 8 and 16 less than a
number
12.The product of 8 more than a number
and 5 less than the number13.The quotient of three times a number
and 10
14.The quotient of 9 and five times a
nonzero numberUse the variable x for the unknown, and write an equation representing the verbal sentence.
Then solve the problem. See Example 1.
15.The sum of a number and 6 is Find the number.
16.The sum of a number and is 18. Find the number.
17.If the product of a number and is subtracted from the number, the result is 9 more than
the number. Find the number.
18.If the quotient of a number and 6 is added to twice the number, the result is 8 less than the
number. Find the number.
19.When of a number is subtracted from 14, the result is 10. Find the number.
20.When 75% of a number is added to 6, the result is 3 more than the number. Find the number.
Decide whether each is an expressionor an equation. Simplify any expressions, and solve any
equations. See Example 2.
Concept Check Complete the six suggested problem-solving steps to solve each problem.
27.In 2008, the corporations securing the most U.S. patents were IBM and Samsung. To-
gether, the two corporations secured a total of 7671 patents, with Samsung receiving 667
fewer patents than IBM. How many patents did each corporation secure? (Source:U.S.
Patent and Trademark Office.)
Step 1 Readthe problem carefully. We are asked to find.
Step 2 Assign a variable.Let the number of patents that IBM secured. Then
the number of.
Step 3 Write an equation.
Step 4 Solvethe equation.
Step 5 State the answer.IBM secured patents, and Samsung secured
patents.
Step 6 Check.The number of Samsung patents was fewer than the number of
, and the total number of patents was.
28.In 2008, 7.8 million more U.S. residents traveled to Mexico than to Canada. There was a
total of 32.8 million U.S. residents traveling to these two countries. How many traveled to
each country? (Source:U.S. Department of Commerce.)
Step 1 Readthe problem carefully. We are asked to find.
Step 2 Assign a variable.Let the number of travelers to Mexico (in millions).
Then the number of.
Step 3 Write an equation.
Step 4 Solvethe equation.
Step 5 State the answer.There were travelers to Mexico and travelers
to Canada.
Step 6 Check.The number of was more than the number of ,
and the total number of these travelers was 20.3+ =.
x=+ =32.8
x-7.8=x=4169 + =
x=+ = 7671
x- 667 =x=1
3
x+1
5
x-1
2
+ 7
1
2
x-1
6
x+3
2
- 8
51 x+ 32 - 812 x- 62 = 12 - 71 x+ 42 + 131 x- 62 = 1851 x+ 32 - 812 x- 62 - 71 x+ 42 + 131 x- 622
3