Problem Solving

Question

A 15 ​-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first​ piece, and the third piece is three inches more than three times the length of the first piece. Find the length of the pieces.

Answer 1

The length of the first piece x is what we will solve for, and the lengths of the other two pieces can be written relative to the first piece:

Second piece is 2x

Third piece is 3x + 3

The lengths of all 3 pieces add up to 15 and can be written as a single equation:

15 = x + 2x + 3x + 3

Combine the x terms first to get:

15 = 6x + 3

Isolate x to get x = 2. This is the length of your first piece. Substitute into your expressions we wrote above to find the length of the other two.

Hope it helps!