The ratio of the amount of money that Jen and Sarah brought along was 4 : 5. For their brother's gift, Jen and Sarah shared the cost in the ratio of 2 : 3. Jen used up
25 of her money to pay for her share. After paying for her share, Sarah had $286 left. How much was the gift?
|
Jen |
Sarah |
Before |
4 u |
5 u |
Change |
- 1.6 u |
- 2.4 u |
Comparing the cost shared between Jen and Sarah |
- 2 p = - 1.6 u |
- 3 p = - 2.4 u |
After |
2.4 u |
286 |
Amount that Jen spent on the gift
=
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 Sarah had left
= 5 u - 2.4 u
= 2.6 u
2.6 u = 286
1 u = 286 ÷ 2.6 = 110
Cost of the gift
= 1.6 u + 2.4 u
= 4 u
= 4 x 110
= $440
Answer: $440