Pierre and Caden have some money. If Pierre gives $216 to Caden, the ratio of their money will be 3 : 5. If Pierre gives $622 to Caden, the ratio of their money will be 1: 4. How much does Pierre have?
| |
Case 1 |
Case 2 |
| |
Pierre |
Caden |
Pierre |
Caden |
| Before |
15 u + $216 |
25 u - $216 |
8 u + $622 |
32 u - $622 |
| Change |
- $216 |
+ $216 |
- $622 |
+ $622 |
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 Pierre has at first is the same in both cases.
15 u + 216 = 8 u + 622
15 u - 8 u = 622 - 216
7 u = 406
1 u = 406 ÷ 7 = 58
Amount that Pierre has
= 15 u + 216
= 15 x 58 + 216
= 870 + 216
= $1086
Answer(s): $1086
