Reggie, Zane and Julian had a total of 107 pens. The ratio of the number of pens that Zane had to the number of pens that Julian had was 4 : 7. After Reggie and Zane each gave away half of their pens, the 3 children had 85 pens left. How many pens did Zane and Julian have at first?
| |
Reggie |
Zane |
Julian |
Total |
| Before |
2 p |
4 u |
7 u |
107 |
| Change |
- 1 p |
- 2 u |
|
- 22 |
| After |
1 p |
2 u |
7 u |
85 |
Total number of pens that Reggie and Zane gave away
= 107 - 85
= 22
1 p + 2 u = 22 --- (1)
1 p + 2 u + 7 u = 85
1 p + 9 u = 85 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 85 - 22
9 u - 2 u = 63
7 u = 63
1 u = 63 ÷ 7 = 9
Total number of pens that Zane and Julian had at first
= 4 u + 7 u
= 11 u
= 11 x 9
= 99
Answer(s): 99
