Gabriel and Elijah have some money. If Gabriel gives $368 to Elijah, the ratio of their money will be 2 : 5. If Gabriel gives $452 to Elijah, the ratio of their money will be 1: 4. How much does Gabriel have?
| |
Case 1 |
Case 2 |
| |
Gabriel |
Elijah |
Gabriel |
Elijah |
| Before |
10 u + $368 |
25 u - $368 |
7 u + $452 |
28 u - $452 |
| Change |
- $368 |
+ $368 |
- $452 |
+ $452 |
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 Gabriel has at first is the same in both cases.
10 u + 368 = 7 u + 452
10 u - 7 u = 452 - 368
3 u = 84
1 u = 84 ÷ 3 = 28
Amount that Gabriel has
= 10 u + 368
= 10 x 28 + 368
= 280 + 368
= $648
Answer(s): $648
