SOLUTION: Bill did 1/5 of his homework problems during study hall. He did 5/8 of the remaining problems at home. Of the questions remaining, he could not do 1/4 of them. What is the ratio of

Question 1189587: Bill did 1/5 of his homework problems during study hall. He did 5/8 of the remaining problems at home. Of the questions remaining, he could not do 1/4 of them. What is the ratio of homework questions he did not know how to do to the homework questions he did know how to do?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the number of homework assignments he had to do in total.
he did 1/5 of his assignments in study hall.
he did 5/8 of the remaining 4/5 of his assignments at home.
total that he did was:
1/5 * x + 5/8 * 4/5 * x = .7 * x
that means he had .3 * x left to do.
of these, he couldn't do 1/4 of them.
that means he could not do 1/4 * .3 = .075 * x.
the total that he could do was (1 - .075) * x = .925 * x.
the ratio of the ones he couldn't do to the ones that he could do is .075 /.925 = 3/37.

to see how this works, assume the total number of homework assignments is 40.
he did 1/5 * 40 = 8 in study hall.
he had 32 left to do.
he did 5/8 * 32 at home = 20
total he did was 8 + 20 = 28.
he had 40 - 28 = 12 left to do.
he couldn't do 1/4 of 12 = 3.
out of the 40, he couldn't do 3 and he could do 37.
the ratio of the ones he couldn't do to the ones he could do was 3/37.

solution looks good.
solution is that the ratio of the ones he couldn't do to the ones he could do is 3/37.

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