Mrs Long had a total of 210 white and purple carnations in the ratio of 9 : 5. After she had given away 6 times as many white carnations as purple carnations, the number of white and purple carnations left was in the ratio of 3 : 2. How many more white carnations than purple carnations did she give away?
|
White |
Purple |
Total |
Before |
9 b |
5 b |
14 b |
Change |
- 6 u |
- 1 u |
|
After |
3 p |
2 p |
|
|
Make p the same (1)x2 = (3) |
White (1) |
Purple (2) |
Make p the same (2)x3 = (4) |
Before |
270 |
135 |
75 |
225 |
Change |
- 12 u |
- 6 u |
- 1 u |
- 3 u |
After |
6 p |
3 p |
2 p |
6 p |
Number of carnations at first
= 9 b + 5 b
= 14 b
14 b = 210
1 b = 210 ÷ 14 = 15
Number of white carnations at first
= 9 b
= 9 x 15
= 135
Number of purple carnations at first
= 5 b
= 5 x 15
= 75
135 - 6 u = 3 p --- (1)
75 - 1 u = 2 p --- (2)
Make p the same.
(1)
x2 270 - 12 u =
6 p --- (3)
(2)
x3 = (4)
225 - 3 u =
6 p --- (4)
(3) = (4)
270 - 12 u = 225 - 3 u
12 u - 3 u = 270 - 225
9 u = 45
1 u = 45 ÷ 9 = 5
Number of more white carnations than purple carnations that she gave away
= 6 u - 1 u
= 5 u
= 5 x 5
= 25
Answer(s): 25