Mrs Neo had a total of 100 yellow and white daisies in the ratio of 7 : 3. After she had given away 5 times as many yellow daisies as white daisies, the number of yellow and white daisies left was in the ratio of 5 : 3. How many more yellow daisies than white daisies did she give away?
|
Yellow |
White |
Total |
Before |
7 b |
3 b |
10 b |
Change |
- 5 u |
- 1 u |
|
After |
5 p |
3 p |
|
|
Make p the same (1)x3 = (3) |
Yellow (1) |
White (2) |
Make p the same (2)x5 = (4) |
Before |
210 |
70 |
30 |
150 |
Change |
- 15 u |
- 5 u |
- 1 u |
- 5 u |
After |
15 p |
5 p |
3 p |
15 p |
Number of daisies at first
= 7 b + 3 b
= 10 b
10 b = 100
1 b = 100 ÷ 10 = 10
Number of yellow daisies at first
= 7 b
= 7 x 10
= 70
Number of white daisies at first
= 3 b
= 3 x 10
= 30
70 - 5 u = 5 p --- (1)
30 - 1 u = 3 p --- (2)
Make p the same.
(1)
x3 210 - 15 u =
15 p --- (3)
(2)
x5 = (4)
150 - 5 u =
15 p --- (4)
(3) = (4)
210 - 15 u = 150 - 5 u
15 u - 5 u = 210 - 150
10 u = 60
1 u = 60 ÷ 10 = 6
Number of more yellow daisies than white daisies that she gave away
= 5 u - 1 u
= 4 u
= 4 x 6
= 24
Answer(s): 24