Xavier and Ian have some money. If Xavier gives $121 to Ian, the ratio of their money will be 3 : 5. If Xavier gives $471 to Ian, the ratio of their money will be 1: 4. How much does Xavier have?
| |
Case 1 |
Case 2 |
| |
Xavier |
Ian |
Xavier |
Ian |
| Before |
15 u + $121 |
25 u - $121 |
8 u + $471 |
32 u - $471 |
| Change |
- $121 |
+ $121 |
- $471 |
+ $471 |
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 Xavier has at first is the same in both cases.
15 u + 121 = 8 u + 471
15 u - 8 u = 471 - 121
7 u = 350
1 u = 350 ÷ 7 = 50
Amount that Xavier has
= 15 u + 121
= 15 x 50 + 121
= 750 + 121
= $871
Answer(s): $871
