Question

Greg has a piece of rope 18 ft long. He wants to cut it into two pieces so that the longer piece (y) is 2 ft less than 3 times the length of the shorter piece (x).

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


A) x - y = 18

B) y = 2 - 3x

C) x + y = 18

D) y = 3x - 2

Answer 1

The required equations are:

C) x + y = 18

D) y = 3x - 2

Explanation:

Let x be the length of shorter piece and y be the length of larger piece

It is given that the total length is 18 ft which gives us our first equation

`x+y = 18`

Now it is also given that

"3 times the length of the shorter piece (x)"

`3x`

"2 ft less than 3 times the length of the shorter piece (x)"

`3x-2`

Second equation will be:

`y = 3x-2`

Hence, the required equations are:

C) x + y = 18

D) y = 3x - 2