Ivory and Hazel have some pens. If Ivory gives 27 pens to Hazel, Hazel will have 5 times the number of pens as Ivory. If Hazel gives 18 pens to Ivory, Ivory will have
25 as many pens as Hazel. How many pens does Ivory have at first?
|
Case 1 |
Case 2 |
|
Ivory |
Hazel |
Ivory |
Hazel |
Before |
7 u + 27 |
35 u - 27 |
12 u - 18 |
30 u + 18 |
Change |
- 27 |
+ 27 |
+ 18 |
- 18 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of pens that Ivory had at first is the same in both cases.
12 u - 18 = 7 u + 27
12 u - 7 u = 27 + 18
5 u = 45
1 u = 9
Number of pens that Ivory had at first
= 7 u + 27
= 7 x 9 + 27
= 63 + 27
= 90
Answer(s): 90