Gillian and Zoe have some erasers. If Gillian gives 34 erasers to Zoe, Zoe will have 5 times the number of erasers as Gillian. If Zoe gives 85 erasers to Gillian, Gillian will have
23 as many erasers as Zoe. How many erasers does Gillian have at first?
| |
Case 1 |
Case 2 |
| |
Gillian |
Zoe |
Gillian |
Zoe |
| Before |
5 u + 34 |
25 u - 34 |
12 u - 85 |
18 u + 85 |
| Change |
- 34 |
+ 34 |
+ 85 |
- 85 |
| 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 Gillian had at first is the same in both cases.
12 u - 85 = 5 u + 34
12 u - 5 u = 34 + 85
7 u = 119
1 u = 17
Number of erasers that Gillian had at first
= 5 u + 34
= 5 x 17 + 34
= 85 + 34
= 119
Answer(s): 119
