Ahmad and Henry have some money. If Ahmad gives $112 to Henry, the ratio of their money will be 3 : 5. If Ahmad gives $553 to Henry, the ratio of their money will be 1: 4. How much does Ahmad have?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Henry |
Ahmad |
Henry |
| Before |
15 u + $112 |
25 u - $112 |
8 u + $553 |
32 u - $553 |
| Change |
- $112 |
+ $112 |
- $553 |
+ $553 |
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 + 112 = 8 u + 553
15 u - 8 u = 553 - 112
7 u = 441
1 u = 441 ÷ 7 = 63
Amount that Ahmad has
= 15 u + 112
= 15 x 63 + 112
= 945 + 112
= $1057
Answer(s): $1057
