Elyse made puffs for sale. 55% of the puffs were chocolate puffs and the rest were beef and sardine puffs in the ratio 4 : 1. If a customer bought 75% of the chocolate puffs and all of the sardine puffs, what percentage of the beef puffs must Elyse 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 |
Beef puffs |
Sardine puffs |
11 u |
9 u |
|
7.2 u |
1.8 u |
|
Chocolate puffs |
Beef puffs |
Sardine puffs |
Total puffs |
Before |
11 u |
7.2 u |
1.8 u |
20 u |
Change |
- 8.25 u |
- 4.95 u |
- 1.8 u |
|
After |
2.75 u |
2.25 u |
0 |
5 u |
55% =
55100 =
112075% =
75100 =
34 Total number of puffs = 20 u
Number of beef and sardine puffs
= 20 u - 11 u
= 9 u
Number of beef puffs at first
=
45 x 9 u
= 7.2 u
Number of sardine puffs at first
= 9 u - 7.2 u
= 1.8 u
Number of chocolate puffs sold
= 75% x 11 u
=
75100 x 11 u
=
34 x 11 u
= 8.25 u
Number of sardine puffs sold
=
15 x 9 u
= 1.8 u
Number of chocolate puffs left
= 11 u - 8.25 u
= 2.75 u
To maintain the percentage of the chocolate puffs in the end,
55% → 2.75 u
100% →
2.7555 x 100 = 5 u
Total number of puffs in the end to maintain the original percentage of chocolate puffs = 5 u
Number of beef puffs left
= 5 u - 2.75 u
= 2.25 u
Number of beef puffs that Elyse must sell to maintain the original percentage of chocolate puffs
= 7.2 u - 2.25 u
= 4.95 u
Percentage of the beef puffs that Elyse must sell
=
4.957.2 x 100%
= 68.8%
Answer(s): 68.8%