Billy and Glen have some money. If Billy gives $280 to Glen, the ratio of their money will be 3 : 5. If Billy gives $686 to Glen, the ratio of their money will be 1: 4. How much does Billy have?
| |
Case 1 |
Case 2 |
| |
Billy |
Glen |
Billy |
Glen |
| Before |
15 u + $280 |
25 u - $280 |
8 u + $686 |
32 u - $686 |
| Change |
- $280 |
+ $280 |
- $686 |
+ $686 |
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 Billy has at first is the same in both cases.
15 u + 280 = 8 u + 686
15 u - 8 u = 686 - 280
7 u = 406
1 u = 406 ÷ 7 = 58
Amount that Billy has
= 15 u + 280
= 15 x 58 + 280
= 870 + 280
= $1150
Answer(s): $1150
