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Question

After Shane had given away 20% of his marbles and Daniel had lost 40% of his marbles, Shane had 16 more marbles than Daniel. It they started with a total of 125 marbles, how many did they have at the start?

Answer

At first,

Shane -> 10S

Daniel -> 10D

10S + 10D = 125 or

60S + 60D = 750 ……… (1)

 

In the end,

Shane -> 10S x 0.8 = 8S

Daniel -> 10D x 0.6 = 6D

8S – 6D = 16 or

80S – 60D = 160 …………(2)

 

(1) + (2) -> 140S = 910

10S = 910 / 14 = 65

10D = 125 – 65 = 60

Shane had 65, Daniel had 60 in the beginning.

1 Reply 1 Like

Thanks for the solution.

How did you get 60D+60S = 750? How to explain this part?

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60D+60S = 750 came straight out of 10D + 10S = 125 by multiply 6 to all terms

 

6 x (10D + 10S) = 6 x 125

60D + 60S = 750

 

Likewise for the second equation.

You get 80S – 60D = 160 by multiplying 10

10 x (8S – 6D) = 10 x 16

 

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