A. One board is one-third the length of another. Six times the sum of the length of the short board and -10 is equal to the length of the longer board decreased by 11 inches. Find the length of the longer board.

Question

B. The length of a rectangle is 4 feet more than twice the width. Five times the width is the same as twice the length increased by 10 feet. Find the dimensions.

C. In February, Paul's electric bill was three dollars more than one-half his gas bill. if the electric bill was ninety-two dollars, what was the gas bill?

Answer 1

B. L=4+2x
W= x+5

5x=2(4+2x)+10
Solve for x and you should get 18.

Length: 40 ft
Width: 23 ft

C. Electric Bill= 3+1/2x
Gas Bill= x
92=3+1/2x
Answer: x=$178

Answer 2

A.
let the longer board be x
shorter board = x/3 or (1/3)x

6(x/3 -10) = x-11
2x - 60 = x -11
x = 49

long board = 49 ft
short board = 49/3 ft

check:
short board is 1/3 of the long one. check!

6(short board - 10)
= 6(49/3 - 10
= 98-60 = 38

longer decreased by 11
= 49-11 = 38
check!