Cindy and Jean have some marbles. If Cindy gives 36 marbles to Jean, Jean will have 4 times the number of marbles as Cindy. If Jean gives 62 marbles to Cindy, Cindy will have
35 as many marbles as Jean. How many marbles does Cindy have at first?
| |
Case 1 |
Case 2 |
| |
Cindy |
Jean |
Cindy |
Jean |
| Before |
8 u + 36 |
32 u - 36 |
15 u - 62 |
25 u + 62 |
| Change |
- 36 |
+ 36 |
+ 62 |
- 62 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 5 and 8 is 40.
Number of marbles that Cindy had at first is the same in both cases.
15 u - 62 = 8 u + 36
15 u - 8 u = 36 + 62
7 u = 98
1 u = 14
Number of marbles that Cindy had at first
= 8 u + 36
= 8 x 14 + 36
= 112 + 36
= 148
Answer(s): 148
