Edgar needed to cut a piece of wood into two smaller segments. The shorter piece was 1 yard longer than half the longer piece. If the length of the entire piece of wood was 7 yards, what is the length of each piece?
Let x be the length of the longer piece of wood. Then the length of the shorter piece is (1/2)x + 1. We know that the entire piece of wood is 7 yards long, so:
x + (1/2)x + 1 = 7
Simplifying:
(3/2)x + 1 = 7
Subtracting 1 from both sides:
(3/2)x = 6
Dividing both sides by 3/2:
x = 4
Therefore, the longer piece of wood is 4 yards long, and the shorter piece is (1/2)4 + 1 = 3 yards long.
Let's assume the longer piece of wood has a length of "x" yards.
According to the problem, the shorter piece is 1 yard longer than half the length of the longer piece.
Therefore, the length of the shorter piece can be calculated as follows:
Shorter piece = (1/2)x + 1
We also know that the length of the entire piece of wood is 7 yards.
So, the equation becomes:
(x/2 + 1) + x = 7
To solve this equation, we can combine like terms:
x/2 + x + 1 = 7
(2x + x)/2 = 7 - 1
(3x)/2 = 6
3x = 12
x = 12/3
x = 4
Therefore, the longer piece of wood is 4 yards.
Now, we can find the length of the shorter piece:
Shorter piece = (1/2)(4) + 1
Shorter piece = 2 + 1
Shorter piece = 3
Hence, the length of the shorter piece is 3 yards and the length of the longer piece is 4 yards.