Joelle and Tiffany have some erasers. If Joelle gives 30 erasers to Tiffany, Tiffany will have 4 times the number of erasers as Joelle. If Tiffany gives 61 erasers to Joelle, Joelle will have
35 as many erasers as Tiffany. How many erasers does Joelle have at first?
|
Case 1 |
Case 2 |
|
Joelle |
Tiffany |
Joelle |
Tiffany |
Before |
8 u + 30 |
32 u - 30 |
15 u - 61 |
25 u + 61 |
Change |
- 30 |
+ 30 |
+ 61 |
- 61 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 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 8 is 40.
Number of erasers that Joelle had at first is the same in both cases.
15 u - 61 = 8 u + 30
15 u - 8 u = 30 + 61
7 u = 91
1 u = 13
Number of erasers that Joelle had at first
= 8 u + 30
= 8 x 13 + 30
= 104 + 30
= 134
Answer(s): 134