Vincent and Ethan had some allowance in the ratio of 5 : 11. They shared some money to buy a necklace for their uncle. The ratio of the amount paid by Vincent to the amount paid by Ethan was 1 : 4. If Ethan was left with $54 and Vincent had spent
25 of his money, how much was the necklace they bought?
| |
Vincent |
Ethan |
| Before |
5 u |
11 u |
| Change |
- 2 u |
- 8 u |
Comparing the
amounts spent |
- 1x2 |
- 4x2 |
| After |
3 u |
54 |
The amount that Vincent spent is repeated. Make the amount that Vincent spent the same. LCM of 1 and 2 is 2.
Amount that Vincent spent
=
25 x 5 u
= 2 u
Amount that Ethan spent
= 4 x 2 u
= 8 u
Amount that Ethan had left
= 11 u - 8 u
= 3 u
3 u = 54
1 u = 54 ÷ 3 = 18
Price of the necklace
= 2 u + 8 u
= 10 u
= 10 x 18
= $180
Answer(s): $180
