Zoe made buns for sale. 60% of the buns were kaya buns and the rest were beef and sardine buns in the ratio 4 : 1. If a customer bought 70% of the kaya buns and all of the sardine buns, what percentage of the beef buns must Zoe sell for her to maintain the original percentage of kaya buns at first? Leave your answer in decimals and correct to 1 decimal place.
Kaya buns |
Beef buns |
Sardine buns |
3 u |
2 u |
|
1.6 u |
0.4 u |
|
Kaya buns |
Beef buns |
Sardine buns |
Total buns |
Before |
3 u |
1.6 u |
0.4 u |
5 u |
Change |
- 2.1 u |
- 1 u |
- 0.4 u |
|
After |
0.9 u |
0.6 u |
0 |
1.5 u |
60% =
60100 =
3570% =
70100 =
710 Total number of buns = 5 u
Number of beef and sardine buns
= 5 u - 3 u
= 2 u
Number of beef buns at first
=
45 x 2 u
= 1.6 u
Number of sardine buns at first
= 2 u - 1.6 u
= 0.4 u
Number of kaya buns sold
= 70% x 3 u
=
70100 x 3 u
=
710 x 3 u
= 2.1 u
Number of sardine buns sold
=
15 x 2 u
= 0.4 u
Number of kaya buns left
= 3 u - 2.1 u
= 0.9 u
To maintain the percentage of the kaya buns in the end,
60% → 0.9 u
100% →
0.960 x 100 = 1.5 u
Total number of buns in the end to maintain the original percentage of kaya buns = 1.5 u
Number of beef buns left
= 1.5 u - 0.9 u
= 0.6 u
Number of beef buns that Zoe must sell to maintain the original percentage of kaya buns
= 1.6 u - 0.6 u
= 1 u
Percentage of the beef buns that Zoe must sell
=
11.6 x 100%
= 62.5%
Answer(s): 62.5%