The ratio of Bart’s marbles to Homer’s marbles is 7:5, before Bart gave away 6 and Homer gave away 30 they had the same amount, how many marbles do they currently have?

Question

Bart gave away 6 and Homer gave away 30.

Answer 1

Before they gave marbles away H=B where H and B are the numbers of marbles each has.

The situation now is Homer has H+30 and Bart has B+6.

The ratio is (B+6)/(H+30)=7/5. But we know B=H, so:

(H+6)/(H+30)=7/5. Cross-multiply: 5H+30=7H+210.

But: 2H=-180 so H=B=-90! This is clearly nonsense.

Let’s reverse the giveaways:

(B+30)/(H+6)=(H+30)/(H+6)=7/5, 5H+150=7H+42, 108=2H so H=B=54 and they currently have H=60 and B=84.

This is a sensible answer and may be the intended answer: Bart gave away 30 marbles and Homer gave away 6.