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A 30-in. board is to be cut into two pieces so that one piece is two-thirds as long as the other piece. Find the length of each piece of board.

User Frank Lee
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Answer:

The length of the longer piece is 18 inches, and the length of the shorter piece is 12 inches.

Explanation:

To find the length of each piece of board, let's assign variables to represent the lengths of the two pieces.

Let x be the length of the longer piece.

Since the other piece is two-thirds as long as the longer piece, we can express the length of the shorter piece as (2/3)x.

We are given that the total length of the board is 30 inches. So, we can write an equation:

x + (2/3)x = 30

To solve this equation, we need to combine like terms:

(5/3)x = 30

Next, we can isolate x by multiplying both sides of the equation by the reciprocal of (5/3), which is (3/5):

x = (3/5)(30)

Simplifying the right side gives us:

x = 18

Therefore, the longer piece of the board has a length of 18 inches.

To find the length of the shorter piece, we substitute the value of x back into the expression for the shorter piece:

(2/3)(18) = 12

Thus, the shorter piece of the board has a length of 12 inches.

In conclusion, the length of the longer piece is 18 inches, and the length of the shorter piece is 12 inches.

User Badaro
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