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.