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Jervin, Ken and Leon shared the cost of a gift for their friend. 1/5 of Jervin's and Leon's share was equal to 2/3 of Ken's share. 3/4 of Leon's share was equal to 1/3 of Jervin's and Ken's share. Leon paid $5 more than Ken. How much did the gift cost?

 Sep 12, 2021
 #1
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Let Jervin share =A

 Ken share = B

Leon share =C

 

From the given information,

1/5th of Jervin's and Leon's share equal to 2/3rd share of Ken's

1/5 (A+C)=2/3(B) 

3A+3C=10B 

3A-10B=-3C      .........(1)

 

1/3th of Jervin's and Ken's share equal to 3/4rd share of Leon's

1/3 (A+B)=3/4 (C)  .

4A+4B=9C               .........(2)

And Leon paid 5 more than Ken

C=B+5

Solving (1) and (2)

4×(1)>>>12A-40B=-12C..........(3)

3×(1)>>>12A+12B=27C  ...........(4)

(4)-(3)>>> (12A+12B)-(12A-40B)=27C+12C

              52B=39C

          4B=3C

Put C=B+5 in above equation

4B=3(B+5)

4B=3B+15

B=15

C=B+5

 =15+5

=20

Put B and C in (2)

4A+4B=9C

4A+4(15)=9(20)

4A=180-60

4A=120

A=30

The gift cost=A+B+C

                      =30+15+20

                      =65

Answer: Gift cost is 65$

 Sep 12, 2021

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