David and Ben had some allowance in the ratio of 3 : 11. They shared some money to buy a ring for their friend. The ratio of the amount paid by David to the amount paid by Ben was 1 : 2. If Ben was left with $161 and David had spent
23 of his money, how much was the ring they bought?
| |
David |
Ben |
| Before |
3 u |
11 u |
| Change |
- 2 u |
- 4 u |
Comparing the
amounts spent |
- 1x2 |
- 2x2 |
| After |
1 u |
161 |
The amount that David spent is repeated. Make the amount that David spent the same. LCM of 1 and 2 is 2.
Amount that David spent
=
23 x 3 u
= 2 u
Amount that Ben spent
= 2 x 2 u
= 4 u
Amount that Ben had left
= 11 u - 4 u
= 7 u
7 u = 161
1 u = 161 ÷ 7 = 23
Price of the ring
= 2 u + 4 u
= 6 u
= 6 x 23
= $138
Answer(s): $138
