Gabby and Sarah have some erasers. If Gabby gives 15 erasers to Sarah, Sarah will have 5 times the number of erasers as Gabby. If Sarah gives 20 erasers to Gabby, Gabby will have
23 as many erasers as Sarah. How many erasers does Gabby have at first?
|
Case 1 |
Case 2 |
|
Gabby |
Sarah |
Gabby |
Sarah |
Before |
5 u + 15 |
25 u - 15 |
12 u - 20 |
18 u + 20 |
Change |
- 15 |
+ 15 |
+ 20 |
- 20 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of erasers that Gabby had at first is the same in both cases.
12 u - 20 = 5 u + 15
12 u - 5 u = 15 + 20
7 u = 35
1 u = 5
Number of erasers that Gabby had at first
= 5 u + 15
= 5 x 5 + 15
= 25 + 15
= 40
Answer(s): 40