Abi and Zoe have some pens. If Abi gives 32 pens to Zoe, Zoe will have 4 times the number of pens as Abi. If Zoe gives 4 pens to Abi, Abi will have
25 as many pens as Zoe. How many pens does Abi have at first?
|
Case 1 |
Case 2 |
|
Abi |
Zoe |
Abi |
Zoe |
Before |
7 u + 32 |
28 u - 32 |
10 u - 4 |
25 u + 4 |
Change |
- 32 |
+ 32 |
+ 4 |
- 4 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 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 7 is 35.
Number of pens that Abi had at first is the same in both cases.
10 u - 4 = 7 u + 32
10 u - 7 u = 32 + 4
3 u = 36
1 u = 12
Number of pens that Abi had at first
= 7 u + 32
= 7 x 12 + 32
= 84 + 32
= 116
Answer(s): 116