Wendy made puffs for sale. 45% of the puffs were chocolate puffs and the rest were chicken and lotus paste puffs in the ratio 3 : 1. If a customer bought 65% of the chocolate puffs and all of the lotus paste puffs, what percentage of the chicken puffs must Wendy sell for her to maintain the original percentage of chocolate puffs at first? Leave your answer in decimals and correct to 1 decimal place.
Chocolate puffs |
Chicken puffs |
Lotus paste puffs |
9 u |
11 u |
|
8.25 u |
2.75 u |
|
Chocolate puffs |
Chicken puffs |
Lotus paste puffs |
Total puffs |
Before |
9 u |
8.25 u |
2.75 u |
20 u |
Change |
- 5.85 u |
- 4.4 u |
- 2.75 u |
|
After |
3.15 u |
3.85 u |
0 |
7 u |
45% =
45100 =
92065% =
65100 =
1320 Total number of puffs = 20 u
Number of chicken and lotus paste puffs
= 20 u - 9 u
= 11 u
Number of chicken puffs at first
=
34 x 11 u
= 8.25 u
Number of lotus paste puffs at first
= 11 u - 8.25 u
= 2.75 u
Number of chocolate puffs sold
= 65% x 9 u
=
65100 x 9 u
=
1320 x 9 u
= 5.85 u
Number of lotus paste puffs sold
=
14 x 11 u
= 2.75 u
Number of chocolate puffs left
= 9 u - 5.85 u
= 3.15 u
To maintain the percentage of the chocolate puffs in the end,
45% → 3.15 u
100% →
3.1545 x 100 = 7 u
Total number of puffs in the end to maintain the original percentage of chocolate puffs = 7 u
Number of chicken puffs left
= 7 u - 3.15 u
= 3.85 u
Number of chicken puffs that Wendy must sell to maintain the original percentage of chocolate puffs
= 8.25 u - 3.85 u
= 4.4 u
Percentage of the chicken puffs that Wendy must sell
=
4.48.25 x 100%
= 53.3%
Answer(s): 53.3%