Vanessa, Xuan and Anna had a total of 70 pens. The ratio of Xuan's pens to Anna's pens was at first 8 : 3. After Vanessa and Xuan each gave half of their pens away, the 3 children had 41 pens left. How many pens did Vanessa and Xuan have at first?
| |
Vanessa |
Xuan |
Anna |
Total |
| Before |
2 p |
8 u |
3 u |
70 |
| Change |
- 1 p |
- 4 u |
|
- 29 |
| After |
1 p |
4 u |
3 u |
41 |
Number of pens that Vanessa and Xuan gave away
= 70 - 41
= 29
1 p + 4 u = 29
1 p = 29 - 4 u --- (1)
1 p + 4 u + 3 u = 41
1 p + 7 u = 41
1 p = 41 - 7 u --- (2)
(1) = (2)
29 - 4 u = 41 - 7 u
7 u - 4 u = 41 - 29
3 u = 12
1 u = 12 ÷ 3 = 4
From (1)
1 p = 29 - 4 u
1 p = 29 - 4 x 4
1 p = 29 - 16 = 13
Number of pens that Vanessa and Xuan had at first
= 2 p + 8 u
= 2 x 13 + 8 x 4
= 26 + 12
= 38
Answer(s): 38
