Xylia made puffs for sale. 45% of the puffs were beef puffs and the rest were lotus paste and sardine puffs in the ratio 4 : 1. If a customer bought 70% of the beef puffs and all of the sardine puffs, what percentage of the lotus paste puffs must Xylia sell for her to maintain the original percentage of beef puffs at first? Leave your answer in decimals and correct to 1 decimal place.
Beef puffs |
Lotus paste puffs |
Sardine puffs |
9 u |
11 u |
|
8.8 u |
2.2 u |
|
Beef puffs |
Lotus paste puffs |
Sardine puffs |
Total puffs |
Before |
9 u |
8.8 u |
2.2 u |
20 u |
Change |
- 6.3 u |
- 5.5 u |
- 2.2 u |
|
After |
2.7 u |
3.3 u |
0 |
6 u |
45% =
45100 =
92070% =
70100 =
710 Total number of puffs = 20 u
Number of lotus paste and sardine puffs
= 20 u - 9 u
= 11 u
Number of lotus paste puffs at first
=
45 x 11 u
= 8.8 u
Number of sardine puffs at first
= 11 u - 8.8 u
= 2.2 u
Number of beef puffs sold
= 70% x 9 u
=
70100 x 9 u
=
710 x 9 u
= 6.3 u
Number of sardine puffs sold
=
15 x 11 u
= 2.2 u
Number of beef puffs left
= 9 u - 6.3 u
= 2.7 u
To maintain the percentage of the beef puffs in the end,
45% → 2.7 u
100% →
2.745 x 100 = 6 u
Total number of puffs in the end to maintain the original percentage of beef puffs = 6 u
Number of lotus paste puffs left
= 6 u - 2.7 u
= 3.3 u
Number of lotus paste puffs that Xylia must sell to maintain the original percentage of beef puffs
= 8.8 u - 3.3 u
= 5.5 u
Percentage of the lotus paste puffs that Xylia must sell
=
5.58.8 x 100%
= 62.5%
Answer(s): 62.5%