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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
 #1
avatar+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 smiley                                        

 May 2, 2021
 #2
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0

That's wrong

Guest May 2, 2021
 #3
avatar+524 
0

Okay, what's wrong?

amygdaleon305  May 2, 2021
 #4
avatar+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
 #5
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+1

I checked at bartebly.com and they had the right answer

Guest May 2, 2021

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