Question

Sasha buys two ribbons of equal length. She cuts 9 pieces of the same length, L, from the first ribbon and finds that 5 inches are left over. She then cuts two pieces of the same length, L, from the second ribbon and finds that 40 inches are left over. What was the length of each ribbon when she bought them?

Answer 1

2 ribbons of equal length (let's call this length x)

first ribbon: original length, minus 9 pieces that are L length each, gives us 5 inches leftover ---> x - 9L = 5

second ribbon: original length, minus 2 pieces that are length L each, gives us 40 inches leftover ---> x - 2L = 40

solve the system for x. there's a couple ways you could do it, but I would subtract the second equation - first equation to eliminate x and solve for L, then plug back into either equation to find x

alternatively, solve each equation for x separately, then set them equal to each other to solve for L, then plug back in to find x