The ratio of the amount of money that Gem and Jane brought along was 4 : 5. For their sister's souvenir, Gem and Jane shared the cost in the ratio of 2 : 3. Gem used up
25 of her money to pay for her share. After paying for her share, Jane had $273 left. How much was the souvenir?
|
Gem |
Jane |
Before |
4 u |
5 u |
Change |
- 1.6 u |
- 2.4 u |
Comparing the cost shared between Gem and Jane |
- 2 p = - 1.6 u |
- 3 p = - 2.4 u |
After |
2.4 u |
273 |
Amount that Gem spent on the souvenir
=
25 x 4 u
= 1.6 u
2 p = 1.6 u
1 p = 1.6 u ÷ 2 = 0.8
3 p = 3 x 0.8 = 2.4 u
Amount that Jane had left
= 5 u - 2.4 u
= 2.6 u
2.6 u = 273
1 u = 273 ÷ 2.6 = 105
Cost of the souvenir
= 1.6 u + 2.4 u
= 4 u
= 4 x 105
= $420
Answer: $420