Ahmad and Bryan have some money. If Ahmad gives $337 to Bryan, the ratio of their money will be 3 : 5. If Ahmad gives $533 to Bryan, the ratio of their money will be 1: 4. How much does Ahmad have?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Bryan |
Ahmad |
Bryan |
| Before |
15 u + $337 |
25 u - $337 |
8 u + $533 |
32 u - $533 |
| Change |
- $337 |
+ $337 |
- $533 |
+ $533 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Ahmad has at first is the same in both cases.
15 u + 337 = 8 u + 533
15 u - 8 u = 533 - 337
7 u = 196
1 u = 196 ÷ 7 = 28
Amount that Ahmad has
= 15 u + 337
= 15 x 28 + 337
= 420 + 337
= $757
Answer(s): $757
