Peter was building a porch. Placinf boards equal length from end to end, Peter found that 4 boards were 3 ft too long for the porch length, while 3 boards were 5 ft too short. How long was each board?
To find the length of each board, let's assume the length of one board as "x" (in feet).
Given that 4 boards were 3 feet too long, it means that the total extra length of these 4 boards combined would be 4 times 3 feet, which is 12 feet.
Similarly, 3 boards were 5 feet too short, implying that the total shortage of length for these 3 boards combined would be 3 times 5 feet, which is 15 feet.
Now, let's set up an equation to solve for the length of each board.
Total extra length - Total shortage of length = 0
(4 * 3) - (3 * 5) = 0
Simplifying the equation:
12 - 15 = 0
-3 = 0
Since the equation doesn't balance, it means we made a mistake in our assumption that x is the length of each board.
Let's try a different approach.
Let's assume the length of each board as "y" (in feet) this time.
We know that 4 boards were 3 feet too long, which means the total extra length for these 4 boards combined would be 4 times 3 feet, which is 12 feet.
Similarly, 3 boards were 5 feet too short, implying that the total shortage of length for these 3 boards combined would be 3 times 5 feet, which is 15 feet.
Now, we can set up another equation to solve for the length of each board.
Total extra length - Total shortage of length = 0
(4 * 3) - (3 * 5) = 0
Simplifying the equation:
12 - 15 = 0
-3 = 0
Once again, the equation doesn't balance.
Considering that both attempts resulted in an equation that cannot balance, it seems there is no solution to this problem. The given information contradicts itself. It is not possible for 4 boards to be too long by 3 feet while 3 other boards are too short by 5 feet.