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

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