Jean and Raeann have some coins. If Jean gives 24 coins to Raeann, Raeann will have 4 times the number of coins as Jean. If Raeann gives 21 coins to Jean, Jean will have
25 as many coins as Raeann. How many coins does Jean have at first?
|
Case 1 |
Case 2 |
|
Jean |
Raeann |
Jean |
Raeann |
Before |
7 u + 24 |
28 u - 24 |
10 u - 21 |
25 u + 21 |
Change |
- 24 |
+ 24 |
+ 21 |
- 21 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 5 and 7 is 35.
Number of coins that Jean had at first is the same in both cases.
10 u - 21 = 7 u + 24
10 u - 7 u = 24 + 21
3 u = 45
1 u = 15
Number of coins that Jean had at first
= 7 u + 24
= 7 x 15 + 24
= 105 + 24
= 129
Answer(s): 129