Pierre and Elijah have some money. If Pierre gives $375 to Elijah, the ratio of their money will be 2 : 5. If Pierre gives $510 to Elijah, the ratio of their money will be 1: 4. How much does Pierre have?
|
Case 1 |
Case 2 |
|
Pierre |
Elijah |
Pierre |
Elijah |
Before |
10 u + $375 |
25 u - $375 |
7 u + $510 |
28 u - $510 |
Change |
- $375 |
+ $375 |
- $510 |
+ $510 |
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 Pierre has at first is the same in both cases.
10 u + 375 = 7 u + 510
10 u - 7 u = 510 - 375
3 u = 135
1 u = 135 ÷ 3 = 45
Amount that Pierre has
= 10 u + 375
= 10 x 45 + 375
= 450 + 375
= $825
Answer(s): $825