Ryan and Zeph have some money. If Ryan gives $224 to Zeph, the ratio of their money will be 3 : 5. If Ryan gives $504 to Zeph, the ratio of their money will be 1: 4. How much does Ryan have?
| |
Case 1 |
Case 2 |
| |
Ryan |
Zeph |
Ryan |
Zeph |
| Before |
15 u + $224 |
25 u - $224 |
8 u + $504 |
32 u - $504 |
| Change |
- $224 |
+ $224 |
- $504 |
+ $504 |
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 Ryan has at first is the same in both cases.
15 u + 224 = 8 u + 504
15 u - 8 u = 504 - 224
7 u = 280
1 u = 280 ÷ 7 = 40
Amount that Ryan has
= 15 u + 224
= 15 x 40 + 224
= 600 + 224
= $824
Answer(s): $824
