Lynn made puffs for sale. 50% of the puffs were beef puffs and the rest were sardine and mushroom puffs in the ratio 4 : 1. If a customer bought 75% of the beef puffs and all of the mushroom puffs, what percentage of the sardine puffs must Lynn 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 |
Sardine puffs |
Mushroom puffs |
1 u |
1 u |
|
0.8 u |
0.2 u |
|
Beef puffs |
Sardine puffs |
Mushroom puffs |
Total puffs |
Before |
1 u |
0.8 u |
0.2 u |
2 u |
Change |
- 0.75 u |
- 0.55 u |
- 0.2 u |
|
After |
0.25 u |
0.25 u |
0 |
0.5 u |
50% =
50100 =
1275% =
75100 =
34 Total number of puffs = 2 u
Number of sardine and mushroom puffs
= 2 u - 1 u
= 1 u
Number of sardine puffs at first
=
45 x 1 u
= 0.8 u
Number of mushroom puffs at first
= 1 u - 0.8 u
= 0.2 u
Number of beef puffs sold
= 75% x 1 u
=
75100 x 1 u
=
34 x 1 u
= 0.75 u
Number of mushroom puffs sold
=
15 x 1 u
= 0.2 u
Number of beef puffs left
= 1 u - 0.75 u
= 0.25 u
To maintain the percentage of the beef puffs in the end,
50% → 0.25 u
100% →
0.2550 x 100 = 0.5 u
Total number of puffs in the end to maintain the original percentage of beef puffs = 0.5 u
Number of sardine puffs left
= 0.5 u - 0.25 u
= 0.25 u
Number of sardine puffs that Lynn must sell to maintain the original percentage of beef puffs
= 0.8 u - 0.25 u
= 0.55 u
Percentage of the sardine puffs that Lynn must sell
=
0.550.8 x 100%
= 68.8%
Answer(s): 68.8%