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.

Guest May 1, 2021

#1**+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 *

amygdaleon305 May 2, 2021

#4**+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