Zeph and Billy have some money. If Zeph gives $141 to Billy, the ratio of their money will be 3 : 5. If Zeph gives $645 to Billy, the ratio of their money will be 1: 4. How much does Zeph have?
| |
Case 1 |
Case 2 |
| |
Zeph |
Billy |
Zeph |
Billy |
| Before |
15 u + $141 |
25 u - $141 |
8 u + $645 |
32 u - $645 |
| Change |
- $141 |
+ $141 |
- $645 |
+ $645 |
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 Zeph has at first is the same in both cases.
15 u + 141 = 8 u + 645
15 u - 8 u = 645 - 141
7 u = 504
1 u = 504 ÷ 7 = 72
Amount that Zeph has
= 15 u + 141
= 15 x 72 + 141
= 1080 + 141
= $1221
Answer(s): $1221
