Zara and Emma have some pens. If Zara gives 15 pens to Emma, Emma will have 4 times the number of pens as Zara. If Emma gives 27 pens to Zara, Zara will have
35 as many pens as Emma. How many pens does Zara have at first?
| |
Case 1 |
Case 2 |
| |
Zara |
Emma |
Zara |
Emma |
| Before |
8 u + 15 |
32 u - 15 |
15 u - 27 |
25 u + 27 |
| Change |
- 15 |
+ 15 |
+ 27 |
- 27 |
| 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 Zara had at first is the same in both cases.
15 u - 27 = 8 u + 15
15 u - 8 u = 15 + 27
7 u = 42
1 u = 6
Number of pens that Zara had at first
= 8 u + 15
= 8 x 6 + 15
= 48 + 15
= 63
Answer(s): 63
