Hugo gave 1/4 of his money and an additional $1 to Calvin. He gave 1/5 of the remaining money and an additional $4 to Kenneth. The amount of money Hugo had left in the end was $31 more than the amount of money he gave to Kenneth. Find the amount of money Hugo gave to Calvin.
+526 Suppose Hugo had \(x\) money at first.
Hugo gave 1/4 of his money and an additional 1 to Cavin
Remaining money with Hugo \(=x-{1\over 4}x-1\)
\(={3\over 4 }x-1\)
He gave 1/5 of the remaining money and an additional 4 to Kenneth
Remaining money with Hugo \(= ({3\over 4}x-1)-{1\over 5}({3\over 4}x-1)-4\)
\(={3\over 4}x-1-{3\over 20}x+{1\over 5}-4\)
\(={12\over 20}x-{24\over 5}\)
Now according to question,
⇒\({12 \over 20}x-{24\over 5}={1\over 5}({3\over4}x-1)+4+31\)
⇒\({12\over 20}x-{24\over 5}={3\over 20}x-{1\over 5}+35\)
⇒\({12\over 20}x-{24\over 5}={3\over 20}x+{174\over 5}\)
⇒\({9\over 20}x={198\over 5}\)
⇒\(x=88\)
∴ Hugo had 88 at first.
Now, amt. of money Hugo gave to Calvin \(={1\over 5}({3\over 4}x-1)+4\)
\(={1\over 5}(65)+4\)
\(=17\)
Thus, Hugo gave 17 units money to Calvin.
~Amy 
+526 No, its absolutely right.
I did reverse answer check here and nothing came out wrong
See? everything fits into the question now what's wrong?
