The length of a string is L inches. Samantha cuts it into two unequal pieces such that the length of the small piece is 35% of L.

If the length of the big piece is 24 inches longer than the length of the small piece, what is the ratio of the length of the small piece to the length of the big piece as a fraction in its lowest terms?

The shorter piece x = 8.4 in

The longer one y = 15.6 in

Step-by-step explanation:

If we cut a string length L in to unequal pieces we get two pieces

first one with length x and the other one with length y

Let call x the smaller piece, then y = L - x will be the longer one

If x = 35 % then

x = 0,35 * L and

y = L - x = L - 0,35*L ⇒ y = 0,65 L ⇒ y = 0.65*24

Now if L = 24 in

x = 0,35*24 ⇒ x = 8.4 in

and

L - x = 0.65*L ⇒ L - x = 0.65*24 y = L - x = 15.6 in

as way of verification you can add the length of the two pieces and find:

8.4 + 15.6 = 24 in