Zeph, Japheth and Justin had a total of 128 pens. The ratio of the number of pens that Japheth had to the number of pens that Justin had was 2 : 9. After Zeph and Japheth each gave away half of their pens, the 3 children had 109 pens left. How many pens did Japheth and Justin have at first?
| |
Zeph |
Japheth |
Justin |
Total |
| Before |
2 p |
2 u |
9 u |
128 |
| Change |
- 1 p |
- 1 u |
|
- 19 |
| After |
1 p |
1 u |
9 u |
109 |
Total number of pens that Zeph and Japheth gave away
= 128 - 109
= 19
1 p + 1 u = 19 --- (1)
1 p + 1 u + 9 u = 109
1 p + 10 u = 109 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 109 - 19
10 u - 1 u = 90
9 u = 90
1 u = 90 ÷ 9 = 10
Total number of pens that Japheth and Justin had at first
= 2 u + 9 u
= 11 u
= 11 x 10
= 110
Answer(s): 110
