Question

A 216​-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece

Answer 1

Let the shorter piece be represented by “p” and the longer piece is five times the length of the other so it can be represented by “5p”. Since the total length of the two pieces together is 216 in., we can write an equation and solve for p: P+ 5p =216.
Combine like terms and solve: 6p=216, divide by 6 on each side which gives you p=36.
The smaller piece, “p”, is 36 inches and the larger piece, “5p” is 5x36 which equals 180.

Answer 2

Let's break this down, step-by-step:

A 216-inch board is cut into two pieces: this is our total length

one piece is five times: let's call the length of this piece 5x, where x is the length of the other piece

the length of the other: this is the length of our shorter piece, which we've decided to give a value of x

find the lengths of the two pieces:

If the total length of the two pieces is 216 inches, then we need to add 5x, the length of our longer piece, to x, the length of our shorter piece, to get 216 = 5x + x.

We combine like terms to get 216 = 6x

Divide both sides by 6 to isolate the variable: 216 ÷ 6 = x

The length of the shorter piece is x = 19 inches

The length of the longer piece is 5x = 95 inches

We can check our work: 114 = 19 + 5(19) = 114 inches.