A 12 foot board is cut into 2 pieces

Question

A 12 foot board is cut into 2 pieces. One piece is three times as long as the other. How long is each piece?

Answer 1

Karla,

If a 12 foot board is cut into two pieces, you’ll have one piece X feet long and another piece Y feet long. In an equation this would look like:

X + Y = 12

Let’s say piece Y is the longer one. If piece Y is 3 times as long as X, in an equation this would look like:

3X = Y

You can then combine these two equations by plugging the second one into the first one.

X + Y = 12 -> X + 3X = 12 -> 4X = 12

To solve for X, divide both sides by 4.

4X = 12 -> X = 3

4 4

Plug this into either equation to solve for Y.

X + Y = 12 -> 3 + Y = 12 -> Y = 9

or

3X = Y -> 3*3 = 9