Ryan and Ian have some money. If Ryan gives $151 to Ian, the ratio of their money will be 3 : 5. If Ryan gives $585 to Ian, the ratio of their money will be 1: 4. How much does Ryan have?
| |
Case 1 |
Case 2 |
| |
Ryan |
Ian |
Ryan |
Ian |
| Before |
15 u + $151 |
25 u - $151 |
8 u + $585 |
32 u - $585 |
| Change |
- $151 |
+ $151 |
- $585 |
+ $585 |
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 + 151 = 8 u + 585
15 u - 8 u = 585 - 151
7 u = 434
1 u = 434 ÷ 7 = 62
Amount that Ryan has
= 15 u + 151
= 15 x 62 + 151
= 930 + 151
= $1081
Answer(s): $1081
