Tammy and Sarah have some erasers. If Tammy gives 16 erasers to Sarah, Sarah will have 4 times the number of erasers as Tammy. If Sarah gives 29 erasers to Tammy, Tammy will have
25 as many erasers as Sarah. How many erasers does Tammy have at first?
|
Case 1 |
Case 2 |
|
Tammy |
Sarah |
Tammy |
Sarah |
Before |
7 u + 16 |
28 u - 16 |
10 u - 29 |
25 u + 29 |
Change |
- 16 |
+ 16 |
+ 29 |
- 29 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 5 and 7 is 35.
Number of erasers that Tammy had at first is the same in both cases.
10 u - 29 = 7 u + 16
10 u - 7 u = 16 + 29
3 u = 45
1 u = 15
Number of erasers that Tammy had at first
= 7 u + 16
= 7 x 15 + 16
= 105 + 16
= 121
Answer(s): 121