Betty and Wendy have some pens. If Betty gives 31 pens to Wendy, Wendy will have 4 times the number of pens as Betty. If Wendy gives 88 pens to Betty, Betty will have
35 as many pens as Wendy. How many pens does Betty have at first?
|
Case 1 |
Case 2 |
|
Betty |
Wendy |
Betty |
Wendy |
Before |
8 u + 31 |
32 u - 31 |
15 u - 88 |
25 u + 88 |
Change |
- 31 |
+ 31 |
+ 88 |
- 88 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 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 8 is 40.
Number of pens that Betty had at first is the same in both cases.
15 u - 88 = 8 u + 31
15 u - 8 u = 31 + 88
7 u = 119
1 u = 17
Number of pens that Betty had at first
= 8 u + 31
= 8 x 17 + 31
= 136 + 31
= 167
Answer(s): 167