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

50 inches.

Explanation:

Let the length of the each ribbon was x.

Now, she cuts 9 pieces of same length L which means total length is 9L.

Now, doing the same she was left with 5 inches of ribbon. Hence, we have

[tex[9L+5=x.....(1)[/tex]

Similarly, we can write a equation for the second situation.

`2L+40=x......(2)`

From equation 1 and 2,

`9L+5=2L+40\\\\7L=35\\\\L=5`

Plugging this value in equation 1,

`9(5)+5=x\\\\x=45+5\\x=50`

Therefore, the length of each ribbon when she bought them was 50 inches.