Question

Peter was building a porch. Placing boards of equal lengths from end to end, Peter found that 4 boards were 3 feet too long for the porch length, while 3 boards were 5 feet too short. How long was each board?

Answer 1

You can write this as two equations, then solve them.
let B be the board length, let T be the total length
so we have...
4B = T+3
3B = T-5

we need to make both equations equal to T, so we can later remove that variable:
T+3 - 3 = 4B - 3
Therefore: T = 4B-3

T-5 + 5 = 3B + 5
Therefore : T = 3B+5

Because they are both equal to T we can make them equal to eachother and reorder the equation to get B on one side:
4B - 3 = 3B + 5
4B - 3 + 3 - 3B = 3B + 5 + 3 - 3B
therefore B = 8

thus we know that the board's length is 8ft long,
Hope this helps! :)