Mrs Song had a total of 156 white and purple lilies in the ratio of 8 : 5. After she had given away 6 times as many white lilies as purple lilies, the number of white and purple lilies left was in the ratio of 6 : 5. How many more white lilies than purple lilies did she give away?
|
White |
Purple |
Total |
Before |
8 b |
5 b |
13 b |
Change |
- 6 u |
- 1 u |
|
After |
6 p |
5 p |
|
|
Make p the same (1)x5 = (3) |
White (1) |
Purple (2) |
Make p the same (2)x6 = (4) |
Before |
480 |
96 |
60 |
360 |
Change |
- 30 u |
- 6 u |
- 1 u |
- 6 u |
After |
30 p |
6 p |
5 p |
30 p |
Number of lilies at first
= 8 b + 5 b
= 13 b
13 b = 156
1 b = 156 ÷ 13 = 12
Number of white lilies at first
= 8 b
= 8 x 12
= 96
Number of purple lilies at first
= 5 b
= 5 x 12
= 60
96 - 6 u = 6 p --- (1)
60 - 1 u = 5 p --- (2)
Make p the same.
(1)
x5 480 - 30 u =
30 p --- (3)
(2)
x6 = (4)
360 - 6 u =
30 p --- (4)
(3) = (4)
480 - 30 u = 360 - 6 u
30 u - 6 u = 480 - 360
24 u = 120
1 u = 120 ÷ 24 = 5
Number of more white lilies than purple lilies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 5
= 25
Answer(s): 25