Mrs Kong had a total of 110 yellow and pink roses in the ratio of 7 : 4. After she had given away 3 times as many yellow roses as pink roses, the number of yellow and pink roses left was in the ratio of 4 : 3. How many more yellow roses than pink roses did she give away?
|
Yellow |
Pink |
Total |
Before |
7 b |
4 b |
11 b |
Change |
- 3 u |
- 1 u |
|
After |
4 p |
3 p |
|
|
Make p the same (1)x3 = (3) |
Yellow (1) |
Pink (2) |
Make p the same (2)x4 = (4) |
Before |
210 |
70 |
40 |
160 |
Change |
- 9 u |
- 3 u |
- 1 u |
- 4 u |
After |
12 p |
4 p |
3 p |
12 p |
Number of roses at first
= 7 b + 4 b
= 11 b
11 b = 110
1 b = 110 ÷ 11 = 10
Number of yellow roses at first
= 7 b
= 7 x 10
= 70
Number of pink roses at first
= 4 b
= 4 x 10
= 40
70 - 3 u = 4 p --- (1)
40 - 1 u = 3 p --- (2)
Make p the same.
(1)
x3 210 - 9 u =
12 p --- (3)
(2)
x4 = (4)
160 - 4 u =
12 p --- (4)
(3) = (4)
210 - 9 u = 160 - 4 u
9 u - 4 u = 210 - 160
5 u = 50
1 u = 50 ÷ 5 = 10
Number of more yellow roses than pink roses that she gave away
= 3 u - 1 u
= 2 u
= 2 x 10
= 20
Answer(s): 20