Ryan and Zeph have some money. If Ryan gives $330 to Zeph, the ratio of their money will be 2 : 5. If Ryan gives $591 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 |
10 u + $330 |
25 u - $330 |
7 u + $591 |
28 u - $591 |
| Change |
- $330 |
+ $330 |
- $591 |
+ $591 |
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 Ryan has at first is the same in both cases.
10 u + 330 = 7 u + 591
10 u - 7 u = 591 - 330
3 u = 261
1 u = 261 ÷ 3 = 87
Amount that Ryan has
= 10 u + 330
= 10 x 87 + 330
= 870 + 330
= $1200
Answer(s): $1200
