7. A 50 foot rope is cut into two pieces, one long piece and one short piece. The length of the long piece is 5 more than 4 times the length of the short piece. What is the length of each piece of rope?

Short piece: 9 ft

Long piece: 41 ft

Step-by-step explanation:

The first step to solving this problem is to translate the given information into some equations. Since we know the total length of the rope is 50 feet, the solution when adding the equation for the short piece and the equation for the long piece must be 50. The information from the second sentence can be translated into a mathematical expression. The phrase "5 more than 4 times" has two key words. They are "times" and "more". "Times" implies multiplication while "more" implies addition. Therefore this sentence becomes the expressions 5+4x, where x is the length of the short piece.

The equations we have from the problem statement are:

L = 5+4x where L represents the length of the long piece and x represents the length of the short piece

x + L = 50

Substituting the equation for the long piece into the equation for total length:

x + (5+4x) = 50

5 + 5x = 50

5x = 45

x = 9 ft

Substituting x = 9 into the equation for the long piece:

L = 5 + 4(9)

L = 5 + 36

L = 41 ft

Checking the answers by substituting x = 9 and L = 41 into the equation for total length:

x + L = 50

9 + 41 = 50

50 = 50