Mrs Neo had a total of 117 purple and white tulips in the ratio of 9 : 4. After she had given away 4 times as many purple tulips as white tulips, the number of purple and white tulips left was in the ratio of 5 : 3. How many more purple tulips than white tulips did she give away?
|
Purple |
White |
Total |
Before |
9 b |
4 b |
13 b |
Change |
- 4 u |
- 1 u |
|
After |
5 p |
3 p |
|
|
Make p the same (1)x3 = (3) |
Purple (1) |
White (2) |
Make p the same (2)x5 = (4) |
Before |
243 |
81 |
36 |
180 |
Change |
- 12 u |
- 4 u |
- 1 u |
- 5 u |
After |
15 p |
5 p |
3 p |
15 p |
Number of tulips at first
= 9 b + 4 b
= 13 b
13 b = 117
1 b = 117 ÷ 13 = 9
Number of purple tulips at first
= 9 b
= 9 x 9
= 81
Number of white tulips at first
= 4 b
= 4 x 9
= 36
81 - 4 u = 5 p --- (1)
36 - 1 u = 3 p --- (2)
Make p the same.
(1)
x3 243 - 12 u =
15 p --- (3)
(2)
x5 = (4)
180 - 5 u =
15 p --- (4)
(3) = (4)
243 - 12 u = 180 - 5 u
12 u - 5 u = 243 - 180
7 u = 63
1 u = 63 ÷ 7 = 9
Number of more purple tulips than white tulips that she gave away
= 4 u - 1 u
= 3 u
= 3 x 9
= 27
Answer(s): 27