Irene and Gillian have some pens. If Irene gives 39 pens to Gillian, Gillian will have 5 times the number of pens as Irene. If Gillian gives 3 pens to Irene, Irene will have
23 as many pens as Gillian. How many pens does Irene have at first?
| |
Case 1 |
Case 2 |
| |
Irene |
Gillian |
Irene |
Gillian |
| Before |
5 u + 39 |
25 u - 39 |
12 u - 3 |
18 u + 3 |
| Change |
- 39 |
+ 39 |
+ 3 |
- 3 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 u |
The total number of pens in both cases remains unchanged. Make the total number of pens in both cases the same. LCM of 6 and 5 is 30.
Number of pens that Irene had at first is the same in both cases.
12 u - 3 = 5 u + 39
12 u - 5 u = 39 + 3
7 u = 42
1 u = 6
Number of pens that Irene had at first
= 5 u + 39
= 5 x 6 + 39
= 30 + 39
= 69
Answer(s): 69
