Ahmad and Caden have some money. If Ahmad gives $159 to Caden, the ratio of their money will be 3 : 5. If Ahmad gives $663 to Caden, the ratio of their money will be 1: 4. How much does Ahmad have?
| |
Case 1 |
Case 2 |
| |
Ahmad |
Caden |
Ahmad |
Caden |
| Before |
15 u + $159 |
25 u - $159 |
8 u + $663 |
32 u - $663 |
| Change |
- $159 |
+ $159 |
- $663 |
+ $663 |
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 + 159 = 8 u + 663
15 u - 8 u = 663 - 159
7 u = 504
1 u = 504 ÷ 7 = 72
Amount that Ahmad has
= 15 u + 159
= 15 x 72 + 159
= 1080 + 159
= $1239
Answer(s): $1239
