A board 60 in. long is cut into two parts so that the longer piece is 5 times the shorter. What are the lengths of the two pieces?

Question

The shorter piece is ___  in.

The longer piece is ____  in.

Answer 1

Let's say that the smaller piece is x. This means that the longer piece is 5x (5 times the shorter length). As stated in the question, we know that the board is 60 inches, and that since the board is cut into two pieces, those two pieces, when put together will be 60 inches. So the equation is 5x + x = 60.

Now, let's solve for x:

5x + x = 60

6x = 60

x = 10

We have officially solved for x, which is 10. At the beginning, we defined the smaller piece as x, so the smaller piece is x = 10 inches. To know how long the bigger piece is, we replace the x in 5x with 10, which will give us 5x = 5(10) = 50. So, the longer piece is 50 inches.

Answer 2

Hi Ashley,

Let's use the variable, x, to represent the length of the shorter piece.

Then we can represent the length of the longer piece with the following expression: 5x

Since the total length is 60 in, we can add this two expressions together and create and solve an equation that shows the total of 60 in:

x + 5x = 60

6x = 60

6x/6 = 60/6

x = 10 inches

The shorter piece will be 10 inches. The longer piece will be 5 x 10 or 50 inches.