Min made sandwiches for sale. 50% of the sandwiches were beef sandwiches and the rest were curry and sardine sandwiches in the ratio 3 : 1. If a customer bought 60% of the beef sandwiches and all of the sardine sandwiches, what percentage of the curry sandwiches must Min sell for her to maintain the original percentage of beef sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.
Beef sandwiches |
Curry sandwiches |
Sardine sandwiches |
1 u |
1 u |
|
0.75 u |
0.25 u |
|
Beef sandwiches |
Curry sandwiches |
Sardine sandwiches |
Total sandwiches |
Before |
1 u |
0.75 u |
0.25 u |
2 u |
Change |
- 0.6 u |
- 0.35 u |
- 0.25 u |
|
After |
0.4 u |
0.4 u |
0 |
0.8 u |
50% =
50100 =
1260% =
60100 =
35 Total number of sandwiches = 2 u
Number of curry and sardine sandwiches
= 2 u - 1 u
= 1 u
Number of curry sandwiches at first
=
34 x 1 u
= 0.75 u
Number of sardine sandwiches at first
= 1 u - 0.75 u
= 0.25 u
Number of beef sandwiches sold
= 60% x 1 u
=
60100 x 1 u
=
35 x 1 u
= 0.6 u
Number of sardine sandwiches sold
=
14 x 1 u
= 0.25 u
Number of beef sandwiches left
= 1 u - 0.6 u
= 0.4 u
To maintain the percentage of the beef sandwiches in the end,
50% → 0.4 u
100% →
0.450 x 100 = 0.8 u
Total number of sandwiches in the end to maintain the original percentage of beef sandwiches = 0.8 u
Number of curry sandwiches left
= 0.8 u - 0.4 u
= 0.4 u
Number of curry sandwiches that Min must sell to maintain the original percentage of beef sandwiches
= 0.75 u - 0.4 u
= 0.35 u
Percentage of the curry sandwiches that Min must sell
=
0.350.75 x 100%
= 46.7%
Answer(s): 46.7%