Practice Translating and Solving Equations Topic Index | Algebra Index | Regents Exam Prep Center

Translate each of the follow sentences into an equation and solve algebraically:

1.
 Ten times a number, increased by 8, is 58. Find the number. Answer Let n = the number. 10n + 8 = 58 10n = 50 n = 5

2.
 A number decreased by 20 equals 46. Find the number. Answer Let n = the number n - 20 = 46 n = 66

3.
 A number divided by 5 equals 18. Find the number. Answer Let n = the number n/5 = 18 n = 90

4.
 If 7 is subtracted from a number, the result is 53. Find the number. Answer Let n = the number n - 7 = 53 n = 60

5.
 If 9 is added to one-half of a number, the result is 29.  Find the number. Answer Let n = the number (1/2)n + 9 = 29 (1/2)n = 20 n = 40

6.
 After he lost 14 pounds, Homer weighed 190 pounds.  Find Homer's original weight. Answer Let w = Homer's original weight. w - 14 = 190 w = 204.

7.
 A shop owner bought 8 dozen shirts.  If he sold all but 18 of them, how many shirts did he sell? Answer 8 dozen = 96 shirts. Let x = shirts sold 96-18 = x 78 = x

8.
 The cost of adding a garage to a home is 5 times as much as the cost of painting the house.  If the garage addition costs \$15,000, find the cost of painting the house. Answer Let p = the cost of painting. 5p = 15000 p = 3000 Cost of painting: \$3000.

9.
 The length of a rectangle is 5 times the width.  If the width is 7 meters, what is the length? Answer Let L = length and W = width. L = 5W L = 5(7) L = 35 meters

10.
 After 2.5 feet had been cut from a piece of lumber, there were 9.5 feet left.  What was the original length of the piece of lumber? Answer Let L = the original length L - 2.5 = 9.5 L = 12 feet.

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