Mrs Tan had a total of 98 yellow and pink carnations in the ratio of 9 : 5. After she had given away 3 times as many yellow carnations as pink carnations, the number of yellow and pink carnations left was in the ratio of 3 : 2. How many more yellow carnations than pink carnations did she give away?
|
Yellow |
Pink |
Total |
Before |
9 b |
5 b |
14 b |
Change |
- 3 u |
- 1 u |
|
After |
3 p |
2 p |
|
|
Make p the same (1)x2 = (3) |
Yellow (1) |
Pink (2) |
Make p the same (2)x3 = (4) |
Before |
126 |
63 |
35 |
105 |
Change |
- 6 u |
- 3 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 = 98
1 b = 98 ÷ 14 = 7
Number of yellow carnations at first
= 9 b
= 9 x 7
= 63
Number of pink carnations at first
= 5 b
= 5 x 7
= 35
63 - 3 u = 3 p --- (1)
35 - 1 u = 2 p --- (2)
Make p the same.
(1)
x2 126 - 6 u =
6 p --- (3)
(2)
x3 = (4)
105 - 3 u =
6 p --- (4)
(3) = (4)
126 - 6 u = 105 - 3 u
6 u - 3 u = 126 - 105
3 u = 21
1 u = 21 ÷ 3 = 7
Number of more yellow carnations than pink carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 7
= 14
Answer(s): 14