Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q13

The ratio of Jane's allowance to Olivia's allowance was 4:3. After Jane and Olivia were given $15 and $8 respectively, the ratio of Jane's allowance to Olivia's allowance became 3:2. How much allowance did Jane have at first?

Solution

Jane
4 units (at first) + $15 (given) --> 3 parts

Olivia
3 units (at first) + $8 --> 2 parts
2 parts --> 3 units + $8
1 part --> 3/2 units + $4
3 parts --> 3 x 3/2 units + 3 x $4
= 9/2 units + $12

(Jane) 3 parts --> 4 units + $15
(Olivia) 3 parts --> 9/2 units + $12

(Olivia) 9/2 units + $12 --> (Jane) 4 units + $15
9/2 units + $12 --> 8/2 units + $15
9/2 units - 8/2 units --> $15 - $12
1/2 unit --> $3
1 unit --> $6

Jane at first
4 units --> 4 x $6 = $24

Answer: $24

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