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# Fraction

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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. May 1, 2021 ### 5+0 Answers #1 +524 +2 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 May 2, 2021 #2 0 That's wrong Guest May 2, 2021 #3 +524 0 Okay, what's wrong? amygdaleon305 May 2, 2021 #4 +524 +2 No, its absolutely right. • Look, we arrived at the solution that Hugo had $$88$$ with him. • He gave 1/4 of his money & an additional 1 to Calvin i.e. $$23$$ • Now he has $$88-23=65$$ remaining with him. • Then he gave 1/5 of remaining and an additional 4 to Kenneth i.e $$17$$ • He has $$65-17=48$$ remaining with him • Now its given that "amount of money Hugo had left in the end was$31 more than the amount of money he gave to Kenneth"
• So, Hugo gave $$17$$ to Kenneth and he has $$48$$ remaining with him.

I did reverse answer check here and nothing came out wrong

See? everything fits into the question now what's wrong?

amygdaleon305  May 2, 2021
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