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Question

Answer

In the end

Jimmy -> 4u

Kelly -> 7u

Given: difference is 72

7u – 4u = 72

3u = 72

u = 24

Jimmy had 4u = 96

Kelly had 7u = 168

Total -> 96 + 168 = 264

Now that we know the actual number of cards, use working backwards

  Jimmy Kelly Total
In the end 96 168 264
Before 2nd loss, ratio was 3:1 3/4 × 264 = 198 1/4  × 264 = 66 264
At first, before Jimmy losing 1/10 198 × 10/9 = 220 264 – 220 = 44 264

(a) Jimmy : Kelly = 220 : 44 = 5 : 1

(b) Kelly won 168 – 44 = 124 cards

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(a)
Jimmy.. : ..Kelly.. : ..Total
In the end,
….4……..:……7.…..:…….11
…16u……:……28u….:…….44u

Before ‘Jimmy lost more cards to Kelly’,
…3……….:………1…..:…….4

…33u……:……11u….:…….44u

28 – 16 = 12
12u ——- 72
1u ——- 6
33u ——- 198

1 – (1/10) = 9/10 ——-198
1/10 ——- 198/9 = 22
10/10 ——- 10 x 22 = 220 (number of cards Jimmy had at first)
11u ——- 11 x 6 = 66
66 – 22 = 44 (number of cards Kelly had at first)
220 : 44 = 5 : 1

(b)
16u ——- 16 x 6 = 96 (number of cards Jimmy had in the end)
220 – 96 = 124
or
28u ——- 28 x 6 = 168 ( number of cards Kelly had in the end)
168 – 44 = 124

Alternatively,
(a)
Jimmy…:…Kelly…:…Total
….5…….:……1.…..:…….6
…55……:……11….:…….66
…10…….:……2…..:…….12
.———……——……———
…-1………….+1
…9…….:…….3
.———……——……———
…-?…………..+?
…4…….:……..7…..:…….11
…24……:…….42….:…….66

42 – 24 = 18
18u ——- 72
1u ——- 4
42 – 11 = 31
31u ——- 124
or
55 – 24 = 31
31u ——- 124

Ans : (a) 5 : 1; (b) 124 cards.

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