Sabrina and Cindy have some erasers. If Sabrina gives 11 erasers to Cindy, Cindy will have 5 times the number of erasers as Sabrina. If Cindy gives 19 erasers to Sabrina, Sabrina will have
25 as many erasers as Cindy. How many erasers does Sabrina have at first?
|
Case 1 |
Case 2 |
|
Sabrina |
Cindy |
Sabrina |
Cindy |
Before |
7 u + 11 |
35 u - 11 |
12 u - 19 |
30 u + 19 |
Change |
- 11 |
+ 11 |
+ 19 |
- 19 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 6 and 7 is 42.
Number of erasers that Sabrina had at first is the same in both cases.
12 u - 19 = 7 u + 11
12 u - 7 u = 11 + 19
5 u = 30
1 u = 6
Number of erasers that Sabrina had at first
= 7 u + 11
= 7 x 6 + 11
= 42 + 11
= 53
Answer(s): 53