Luis and Jack had 350 marbles altogether. Luis gave away 25% as many marbles as Jack. Jack was left with 40 more than the number of marbles he gave away? Luis had 25% as many marbles as Jack in the end. How many marbles did Jack have in the end?
+128408 Let the number that Jack gave away = G
Then Luis gave away .25G
Number that Jack had remaining = G + 40
So Jack must have started with G + G + 40 = 2G + 40
And Luis must have started with (.25)G + .25(G + 40) = .5G + 10
So
(2G + 40) + (.5G + 10) = 350
2.5G + 50 = 350
2.5G = 350 - 50
2.5G = 300
G = 300 / 2.5
G = 120
Jack had 120 + 40 = 160 at the end
Proof
Jack started with 2(120) + 40 = 280
Luis started with .5(120) + 10 = 70
Jack gave away 120 and ended up with 160 = 40 more than he gave away
Luis gave away (.25)(120) = 30
And he ended up with 40 = .25 of (160)
