Ahmad and Owen have some money. If Ahmad gives $295 to Owen, the ratio of their money will be 2 : 5. If Ahmad gives $613 to Owen, the ratio of their money will be 1: 4. How much does Ahmad have?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Owen |
Ahmad |
Owen |
| Before |
10 u + $295 |
25 u - $295 |
7 u + $613 |
28 u - $613 |
| Change |
- $295 |
+ $295 |
- $613 |
+ $613 |
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 + 295 = 7 u + 613
10 u - 7 u = 613 - 295
3 u = 318
1 u = 318 ÷ 3 = 106
Amount that Ahmad has
= 10 u + 295
= 10 x 106 + 295
= 1060 + 295
= $1355
Answer(s): $1355
