Hazel made croissants for sale. 60% of the croissants were kaya croissants and the rest were beef and sardine croissants in the ratio 3 : 1. If a customer bought 75% of the kaya croissants and all of the sardine croissants, what percentage of the beef croissants must Hazel sell for her to maintain the original percentage of kaya croissants at first? Leave your answer in decimals and correct to 1 decimal place.
Kaya croissants |
Beef croissants |
Sardine croissants |
3 u |
2 u |
|
1.5 u |
0.5 u |
|
Kaya croissants |
Beef croissants |
Sardine croissants |
Total croissants |
Before |
3 u |
1.5 u |
0.5 u |
5 u |
Change |
- 2.25 u |
- 1 u |
- 0.5 u |
|
After |
0.75 u |
0.5 u |
0 |
1.25 u |
60% =
60100 =
3575% =
75100 =
34 Total number of croissants = 5 u
Number of beef and sardine croissants
= 5 u - 3 u
= 2 u
Number of beef croissants at first
=
34 x 2 u
= 1.5 u
Number of sardine croissants at first
= 2 u - 1.5 u
= 0.5 u
Number of kaya croissants sold
= 75% x 3 u
=
75100 x 3 u
=
34 x 3 u
= 2.25 u
Number of sardine croissants sold
=
14 x 2 u
= 0.5 u
Number of kaya croissants left
= 3 u - 2.25 u
= 0.75 u
To maintain the percentage of the kaya croissants in the end,
60% → 0.75 u
100% →
0.7560 x 100 = 1.25 u
Total number of croissants in the end to maintain the original percentage of kaya croissants = 1.25 u
Number of beef croissants left
= 1.25 u - 0.75 u
= 0.5 u
Number of beef croissants that Hazel must sell to maintain the original percentage of kaya croissants
= 1.5 u - 0.5 u
= 1 u
Percentage of the beef croissants that Hazel must sell
=
11.5 x 100%
= 66.7%
Answer(s): 66.7%