Find the length of each piece

Question

The carpenter saws a board that is 22 feet long into two pieces. One piece is to be 4 feet longer than twice the length of the shorter piece. Find the length of each piece. 

Answer 1

Call the two pieces x and y.

x + y = 22

x = 2y + 4 (2y is twice the length of the shorter piece. 4 feet longer means add 4)

Now that you have two equations, you can substitute 2y + 4 for the x in the first equation.

2y + 4 + y = 22

Now that you only have one variable, y, you can solve the equation.

Combine like terms: 3y + 4 = 22

Subtract 4 from both sides: 3y = 18

Divide both sides by 3: y = 6

Now that you know y is 6, you can plug it back into either equation to solve for x.

x + y = 22

x + 6 = 22

Subtract 6 from both sides: x = 16

The two sides are 16 and 6 feet long.