Question

(((ASAP))) David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece (y) is 3 ft more than 2 times the length of the shorter piece (x).

Choose the two equations that will create our system of equations for this story problem.


y = 3 + 2y

x - y = 27

x + y = 27

y = 3y - 2

Answer 1

Let the length of shorter piece be x ft.

so '' '' '' '' '' '' = 2 x + 3

A/Q, x + 2 x + 3 = 27

3 x = 24

x = 8

Length of shorter piece = x = 8 ft.

'' '' longer '' = 2 x + 3 = 16 +3 = 19 ft.

Explanation:

let x and y be the length of the longer and the shorter pieces of the hose respectively.

By question,

x + y = 27 --- (1)

and,

x - 2y = 3 --- (2)

subtracting (1) by (2), we get,

y-(-2y) = 27-3

=> 3y = 24

=> y = 24/3

=> y = 8

putting y = 8 in (1)

x + 8 = 27

=> x = 27-8

=> x = 19

Therefore, the length of the shorter piece is 8 ft and the length of the longer piece is 19 ft