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

Answer 1

The length of the longer rope piece is 14 ft

Explanation:

Let

x -----> the longer piece

y ----> the shorter piece

we know that

The sum of the longer piece plus the shorter piece must be equal to the length of the original piece

x+y=21

y=(21-x) -----> equation A

3x-7=5y ----> equation B

substitute equation A in equation B and solve for x

therefore

The length of the longer rope piece is 14 ft

Answer 2

simultaneous equations

Explanation:

a = 5b - 2

a +2 =5b

+2 = 5b - a

:. 5b - a = 2-------(1)

a + b = 100 -------(2)

from (1)

a = 5b - 2

so substituting a = 5b - 2 in (2) we get

5b - 2 + b = 100

6b = 102

b = 102/6

= 17

so from (2)

a + b = 100

a = 100 - b

= 83