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(a)
Let the number of bookmarks and stickers be 2u and 2p respectively.
Jason :
bookmarks : 2u – 1u – 7 = 1u – 7
stickers : 1p

(1u – 7) x 9 = 9u – 63 ——-> 1p

Kelvin :
bookmarks : 1u
stickers : 2p – 1p – 12 = 1p – 12

1u x 6 = 6u——-> 1p – 12

9u – 63 = 6u + 12
1u = (12 + 63)/(9 – 6) = 25
1p – 12 = 6 x 25 = 150

(b)
2u = 2 x 25 = 50

Ans : (a) 150 stickers; (b) 50 bookmarks.

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At first, Jason bought 2b of bookmarks and Kelvin bought 2s of stickers.

After the exchange, Jason and Kelvin each will have (b+s) bookmarks and stickers.

When Jason gave 7 bookmarks to his sister, he will be left with (b-7) bookmarks.

9(b-7) -> s

When Kelvin gave 12 stickers to his youger brother, he will be left with (s-12) stickers.

6b -> (s-12) or b -> s/6 – 2

9(s/6 – 2 – 7) -> s

1.5s – 81 -> s

s -> 162

a) At end, number of stickers Kelvin has -> 162 – 12 = 150

b) At the beginning, number of bookmarks Jason bought -> 2b -> (162/6 -2) x 2 = 50

 

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