Mrs Kok had a total of 209 yellow and white roses in the ratio of 7 : 4. After she had given away 5 times as many yellow roses as white roses, the number of yellow and white roses left was in the ratio of 6 : 5. How many more yellow roses than white roses did she give away?
|
Yellow |
White |
Total |
Before |
7 b |
4 b |
11 b |
Change |
- 5 u |
- 1 u |
|
After |
6 p |
5 p |
|
|
Make p the same (1)x5 = (3) |
Yellow (1) |
White (2) |
Make p the same (2)x6 = (4) |
Before |
665 |
133 |
76 |
456 |
Change |
- 25 u |
- 5 u |
- 1 u |
- 6 u |
After |
30 p |
6 p |
5 p |
30 p |
Number of roses at first
= 7 b + 4 b
= 11 b
11 b = 209
1 b = 209 ÷ 11 = 19
Number of yellow roses at first
= 7 b
= 7 x 19
= 133
Number of white roses at first
= 4 b
= 4 x 19
= 76
133 - 5 u = 6 p --- (1)
76 - 1 u = 5 p --- (2)
Make p the same.
(1)
x5 665 - 25 u =
30 p --- (3)
(2)
x6 = (4)
456 - 6 u =
30 p --- (4)
(3) = (4)
665 - 25 u = 456 - 6 u
25 u - 6 u = 665 - 456
19 u = 209
1 u = 209 ÷ 19 = 11
Number of more yellow roses than white roses that she gave away
= 5 u - 1 u
= 4 u
= 4 x 11
= 44
Answer(s): 44