Ivory, Emma and Olivia had a total of 166 pens. The ratio of Emma's pens to Olivia's pens was at first 4 : 7. After Ivory and Emma each gave half of their pens away, the 3 children had 125 pens left. How many pens did Ivory and Emma have at first?
| |
Ivory |
Emma |
Olivia |
Total |
| Before |
2 p |
4 u |
7 u |
166 |
| Change |
- 1 p |
- 2 u |
|
- 41 |
| After |
1 p |
2 u |
7 u |
125 |
Number of pens that Ivory and Emma gave away
= 166 - 125
= 41
1 p + 2 u = 41
1 p = 41 - 2 u --- (1)
1 p + 2 u + 7 u = 125
1 p + 9 u = 125
1 p = 125 - 9 u --- (2)
(1) = (2)
41 - 2 u = 125 - 9 u
9 u - 2 u = 125 - 41
7 u = 84
1 u = 84 ÷ 7 = 12
From (1)
1 p = 41 - 2 u
1 p = 41 - 2 x 12
1 p = 41 - 24 = 17
Number of pens that Ivory and Emma had at first
= 2 p + 4 u
= 2 x 17 + 4 x 12
= 34 + 84
= 118
Answer(s): 118
