Cathy, Lynn and Jaslyn had a total of 132 pens. The ratio of Lynn's pens to Jaslyn's pens was at first 4 : 3. After Cathy and Lynn each gave half of their pens away, the 3 children had 84 pens left. How many pens did Cathy and Jaslyn have at first?
| |
Cathy |
Lynn |
Jaslyn |
Total |
| Before |
2 p |
4 u |
3 u |
132 |
| Change |
- 1 p |
- 2 u |
|
- 48 |
| After |
1 p |
2 u |
3 u |
84 |
Number of pens that Cathy and Lynn gave away
= 132 - 84
= 48
1 p + 2 u = 48
1 p = 48 - 2 u --- (1)
1 p + 2 u + 3 u = 84
1 p + 5 u = 84
1 p = 84 - 5 u --- (2)
(1) = (2)
48 - 2 u = 84 - 5 u
5 u - 2 u = 84 - 48
3 u = 36
1 u = 36 ÷ 3 = 12
From (1)
1 p = 48 - 2 u
1 p = 48 - 2 x 12
1 p = 48 - 24 = 24
Number of pens that Cathy and Jaslyn had at first
= 2 p + 3 u
= 2 x 24 + 3 x 12
= 48 + 36
= 84
Answer(s): 84
