Mary and Hazel have some pens. If Mary gives 21 pens to Hazel, Hazel will have 4 times the number of pens as Mary. If Hazel gives 5 pens to Mary, Mary will have
12 as many pens as Hazel. How many pens does Mary have at first?
| |
Case 1 |
Case 2 |
| |
Mary |
Hazel |
Mary |
Hazel |
| Before |
3 u + 21 |
12 u - 21 |
5 u - 5 |
10 u + 5 |
| Change |
- 21 |
+ 21 |
+ 5 |
- 5 |
| After |
1x3 =
3 u |
4x3 =
12 u |
1x5 =
5 u |
2x5 =
10 u |
The total number of pens in both cases remains unchanged. Make the total number of pens in both cases the same. LCM of 5 and 3 is 15.
Number of pens that Mary had at first is the same in both cases.
5 u - 5 = 3 u + 21
5 u - 3 u = 21 + 5
2 u = 26
1 u = 13
Number of pens that Mary had at first
= 3 u + 21
= 3 x 13 + 21
= 39 + 21
= 60
Answer(s): 60
