Zeph and Eric have some money. If Zeph gives $278 to Eric, the ratio of their money will be 2 : 5. If Zeph gives $563 to Eric, the ratio of their money will be 1: 4. How much does Zeph have?
| |
Case 1 |
Case 2 |
| |
Zeph |
Eric |
Zeph |
Eric |
| Before |
10 u + $278 |
25 u - $278 |
7 u + $563 |
28 u - $563 |
| Change |
- $278 |
+ $278 |
- $563 |
+ $563 |
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 Zeph has at first is the same in both cases.
10 u + 278 = 7 u + 563
10 u - 7 u = 563 - 278
3 u = 285
1 u = 285 ÷ 3 = 95
Amount that Zeph has
= 10 u + 278
= 10 x 95 + 278
= 950 + 278
= $1228
Answer(s): $1228
