Elijah and Tommy have some money. If Elijah gives $351 to Tommy, the ratio of their money will be 2 : 5. If Elijah gives $543 to Tommy, the ratio of their money will be 1: 4. How much does Elijah have?
| |
Case 1 |
Case 2 |
| |
Elijah |
Tommy |
Elijah |
Tommy |
| Before |
10 u + $351 |
25 u - $351 |
7 u + $543 |
28 u - $543 |
| Change |
- $351 |
+ $351 |
- $543 |
+ $543 |
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 Elijah has at first is the same in both cases.
10 u + 351 = 7 u + 543
10 u - 7 u = 543 - 351
3 u = 192
1 u = 192 ÷ 3 = 64
Amount that Elijah has
= 10 u + 351
= 10 x 64 + 351
= 640 + 351
= $991
Answer(s): $991
