Emily, Victoria and Yen had a total of 146 pens. The ratio of Victoria's pens to Yen's pens was at first 4 : 7. After Emily and Victoria each gave half of their pens away, the 3 children had 108 pens left. How many pens did Emily and Victoria have at first?
| |
Emily |
Victoria |
Yen |
Total |
| Before |
2 p |
4 u |
7 u |
146 |
| Change |
- 1 p |
- 2 u |
|
- 38 |
| After |
1 p |
2 u |
7 u |
108 |
Number of pens that Emily and Victoria gave away
= 146 - 108
= 38
1 p + 2 u = 38
1 p = 38 - 2 u --- (1)
1 p + 2 u + 7 u = 108
1 p + 9 u = 108
1 p = 108 - 9 u --- (2)
(1) = (2)
38 - 2 u = 108 - 9 u
9 u - 2 u = 108 - 38
7 u = 70
1 u = 70 ÷ 7 = 10
From (1)
1 p = 38 - 2 u
1 p = 38 - 2 x 10
1 p = 38 - 20 = 18
Number of pens that Emily and Victoria had at first
= 2 p + 4 u
= 2 x 18 + 4 x 10
= 36 + 70
= 106
Answer(s): 106
