Question

Keith won a cash prize in an art competition. He gave his mother 2/5 of the money he won. Of the remainder, 1/4 was given to his sister, and 2/3 was given to his brother. He had $15 left. How much was Keith’s cash prize?

please give me an explanation (I need it)

Answer 1

300 dollars

Explanation:

Let the original amount = x

x - 2/5x was what his mother's share looked.

5/5 x - 2/5 x

3/5x is what is left.

3/5 x - 1/4 * 3/5 x - 2/3x * 3/5 = his sister's share and his brothers

3/5x - 1/4*3/5 x - 2/3 * 3/5 = 15

3/5x * (1 - 1/4 - 2/3) = 15

3/5 x 5/60 = 15

15 / 300 * x = 15

1/20 x = 15

x = 15 * 20

x = 300