**Adam and Ben each have some money. If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5. If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13. How much money does each boy have?***(click on image to enlarge)*

- If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5, hence,**Adam has 3 units** (after $4 spent), while **Ben has 5 units** (marked in blue in illustration above).

- If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13, hence,**Adam** now has been allocated **11 parts**, while **Ben** has been allocated **13 parts** (after $4 spent by Ben), as marked in red in llustration above.

From here, we can deduce

2 units ----- $4 + 2 parts $4

2 units ----- $8 + 2 parts

1 unit ----- $4 + 1 parts**3 units ----- $12 + 3 parts (*)**

However, we know that

(Adam) **3 units ----- 11 parts - $4 (#)** (as from model above)

Both * and # have an equivalent of 3 units. Therefore,

$12 + 3 parts (*) ----- 11 parts - $4 (#)

$16 ----- 8 parts**1 part** ----- $16 divided by 8 = **$2****Adam** has ---- 11 parts

= (11 parts x $2)

= **$22****Ben** has ----- 13 parts + $4

= (13 parts x $2) + $4

= $26 + $4

= **$30****Answer: Adam has $22, while Ben has $30.**

This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Saturday, November 10, 2007

### Raffles Girls’ Primary School P5 SA1 2007 Math Question

Labels:
Mathematics,
Ratio

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