Ahmad and Daniel have some money. If Ahmad gives $196 to Daniel, the ratio of their money will be 2 : 5. If Ahmad gives $463 to Daniel, the ratio of their money will be 1: 4. How much does Ahmad have?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Daniel |
Ahmad |
Daniel |
| Before |
10 u + $196 |
25 u - $196 |
7 u + $463 |
28 u - $463 |
| Change |
- $196 |
+ $196 |
- $463 |
+ $463 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Ahmad has at first is the same in both cases.
10 u + 196 = 7 u + 463
10 u - 7 u = 463 - 196
3 u = 267
1 u = 267 ÷ 3 = 89
Amount that Ahmad has
= 10 u + 196
= 10 x 89 + 196
= 890 + 196
= $1086
Answer(s): $1086
