Risa, Cindy and Hilda had a total of 213 pens. The ratio of Cindy's pens to Hilda's pens was at first 8 : 7. After Risa and Cindy each gave half of their pens away, the 3 children had 145 pens left. How many pens did Risa and Cindy have at first?
| |
Risa |
Cindy |
Hilda |
Total |
| Before |
2 p |
8 u |
7 u |
213 |
| Change |
- 1 p |
- 4 u |
|
- 68 |
| After |
1 p |
4 u |
7 u |
145 |
Number of pens that Risa and Cindy gave away
= 213 - 145
= 68
1 p + 4 u = 68
1 p = 68 - 4 u --- (1)
1 p + 4 u + 7 u = 145
1 p + 11 u = 145
1 p = 145 - 11 u --- (2)
(1) = (2)
68 - 4 u = 145 - 11 u
11 u - 4 u = 145 - 68
7 u = 77
1 u = 77 ÷ 7 = 11
From (1)
1 p = 68 - 4 u
1 p = 68 - 4 x 11
1 p = 68 - 44 = 24
Number of pens that Risa and Cindy had at first
= 2 p + 8 u
= 2 x 24 + 8 x 11
= 48 + 77
= 125
Answer(s): 125
