Dylan, Simon and Zeph had a total of 30 pens. The ratio of the number of pens that Simon had to the number of pens that Zeph had was 4 : 7. After Dylan and Simon each gave away half of their pens, the 3 children had 22 pens left. How many pens did Simon and Zeph have in the end?
| |
Dylan |
Simon |
Zeph |
Total |
| Before |
2 p |
4 u |
7 u |
30 |
| Change |
- 1 p |
- 2 u |
|
- 8 |
| After |
1 p |
2 u |
7 u |
22 |
Total number of pens that Dylan and Simon gave away
= 30 - 22
= 8
1 p + 2 u = 8 --- (1)
1 p + 2 u + 7 u = 22
1 p + 9 u = 22 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 22 - 8
9 u - 2 u = 14
7 u = 14
1 u = 14 ÷ 7 = 2
Total number of pens that Simon and Zeph had in the end
= 2 u + 7 u
= 9 u
= 9 x 2
= 18
Answer(s): 18
