Elijah and Zane have some money. If Elijah gives $117 to Zane, the ratio of their money will be 3 : 5. If Elijah gives $516 to Zane, the ratio of their money will be 1: 4. How much does Elijah have?
| |
Case 1 |
Case 2 |
| |
Elijah |
Zane |
Elijah |
Zane |
| Before |
15 u + $117 |
25 u - $117 |
8 u + $516 |
32 u - $516 |
| Change |
- $117 |
+ $117 |
- $516 |
+ $516 |
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 Elijah has at first is the same in both cases.
15 u + 117 = 8 u + 516
15 u - 8 u = 516 - 117
7 u = 399
1 u = 399 ÷ 7 = 57
Amount that Elijah has
= 15 u + 117
= 15 x 57 + 117
= 855 + 117
= $972
Answer(s): $972
