Question

A 30-in. board is to be cut into two pieces so that one piece is two-thirds as long as the other piece. What are the possible lengths of the board?

a) 10 in and 20 in
b) 12 in and 18 in
c) 15 in and 15 in
d) 20 in and 10 in

Answer 1

To find the possible lengths of the board, assume the length of one piece is x inches. According to the given information, the length of the other piece is two-thirds as long. Together, these two pieces should add up to 30 inches. Solve the equation to find the lengths of the two pieces.

Step-by-step explanation:

To find the possible lengths of the board, let's assume the length of one piece is x inches. According to the given information, the length of the other piece is two-thirds as long, so it would be (2/3)x inches. Together, these two pieces should add up to 30 inches, so the equation becomes x + (2/3)x = 30.

Simplifying the equation, we have (5/3)x = 30. To solve for x, we can multiply both sides of the equation by 3/5, giving us x = (3/5) * 30 = 18 inches. Therefore, one piece is 18 inches long, and the other piece is (2/3) * 18 = 12 inches long.