Eric and Japheth have some money. If Eric gives $114 to Japheth, the ratio of their money will be 2 : 5. If Eric gives $537 to Japheth, the ratio of their money will be 1: 4. How much does Eric have?
|
Case 1 |
Case 2 |
|
Eric |
Japheth |
Eric |
Japheth |
Before |
10 u + $114 |
25 u - $114 |
7 u + $537 |
28 u - $537 |
Change |
- $114 |
+ $114 |
- $537 |
+ $537 |
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 Eric has at first is the same in both cases.
10 u + 114 = 7 u + 537
10 u - 7 u = 537 - 114
3 u = 423
1 u = 423 ÷ 3 = 141
Amount that Eric has
= 10 u + 114
= 10 x 141 + 114
= 1410 + 114
= $1524
Answer(s): $1524