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Question

Mary and Joseph went shopping together with a total sum of $99. Mary spent twice as much as Joseph. The amount of money Joseph had left was $12 more than what he had spent. He had twice as much money left as Mary. How much did Joseph have at first?

Source: Maha Bodhi

Answer

spent —
Mary : 4u
Joseph : 2u
left —
Mary : 1u + 6
Joseph : 2u + 12
2u + 12 + 1u + 6 + 2u + 4u = 9u + 18 ——- 99
1u ——- (99 – 18)/9 = 9
2u + 2u + 12 = 4u + 12 ——- 4 x 9 + 12 = 48

or alternatively,
spent —
Mary : 2u
Joseph : 1u
left —
Mary : 0.5u + 6
Joseph : 1u + 12

2u + 1u + 0.5u + 6 + 1u + 12 = 5.5u + 18 ——- 99
1u ——- (99 – 18)/5.5 = 18
1u + 1u + 12 = 2u + 12 ——- 2 x 18 + 12 = 48

Ans : $48.

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  Joseph Mary
Money Spent 2u 4u
Money Left

($12 more than what he spent)

2u + 12

(half of what Joseph had left)

(2u + 12) ÷ 2 = 1u + 6

Money at first 

(Money spent + money left)

4u + 12 5u + 6

Money at first -> (4u + 12) + (5u + 6) = 9u + 18

9u + 18 = 99

9u = 81

1u = 9

At first, Joseph had (4u + 12) = 36 + 12 = $48

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