Billy and Pierre have some money. If Billy gives $269 to Pierre, the ratio of their money will be 2 : 5. If Billy gives $554 to Pierre, the ratio of their money will be 1: 4. How much does Billy have?
| |
Case 1 |
Case 2 |
| |
Billy |
Pierre |
Billy |
Pierre |
| Before |
10 u + $269 |
25 u - $269 |
7 u + $554 |
28 u - $554 |
| Change |
- $269 |
+ $269 |
- $554 |
+ $554 |
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 Billy has at first is the same in both cases.
10 u + 269 = 7 u + 554
10 u - 7 u = 554 - 269
3 u = 285
1 u = 285 ÷ 3 = 95
Amount that Billy has
= 10 u + 269
= 10 x 95 + 269
= 950 + 269
= $1219
Answer(s): $1219
