Question

Jim had (5w + 10) marbles. The number of marbles Joe had was 1/5 of what Jim had and Mike had (3w + 12) marbles. How many marbles, in terms of w, did each of them have if they shared the marbles equally?

Answer 1

The number of marbles Joe had was 1/5 of what Jim had, which is (1/5)(5w + 10) = w + 2.

Together, Jim and Joe had (5w + 10) + (w + 2) = 6w + 12 marbles.

If Mike had (3w + 12) marbles, then the total number of marbles was (6w + 12) + (3w + 12) = 9w + 24.

If they shared the marbles equally, each of them would have (9w + 24)/(3) = 3w + 8 marbles.

Therefore, Jim had 5w + 10 = (3w + 8) - (w + 2) marbles.

Joe had w + 2 = (3w + 8)/(5) marbles.

Mike had 3w + 12 = (3w + 8) + 4 marbles.