Question

1. A 100-foot rope is cut into 2 pieces (a and b). Piece a is 2ft less than 5 times the length of piece b. (a) What is the system that models this situation? (b) Solve the system of equations


PLEASE HELP I WILL GIVE YOU 100PTS IF YOU HELP ME AND ANSWER THIS QUESTION

Answer 1

Answer:

Represent the longer piece of the rope as (18 + x) and the shorter piece as x. The rope is 100 feet long, so:

(18 + x) + x = 100      Set up equation

18 + x + x = 100        Arrange like terms

18 + 2x = 100            Combine like terms

2x = 82                     Subtract 18 from both sides

x = 41                       Divide both sides by 2

Longer rope length: 12+ 31 =43 feet

Shorter rope length: 57 feet

Check: 59 + 41 = 100 feet

Step-by-step explanation:

Answer 2

Answer/Step-by-step explanation:

100 divided by 2 = 50

rope a 50 divided by 10 = 5 - 2 = 3 ft

rope b 100 - 3 = 97

change 9 to 5

and change 3 to 43

a = 43

b = 57