Fanny made sandwiches for sale. 50% of the sandwiches were lotus paste sandwiches and the rest were chocolate and curry sandwiches in the ratio 3 : 1. If a customer bought 80% of the lotus paste sandwiches and all of the curry sandwiches, what percentage of the chocolate sandwiches must Fanny sell for her to maintain the original percentage of lotus paste sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.
Lotus paste sandwiches |
Chocolate sandwiches |
Curry sandwiches |
1 u |
1 u |
|
0.75 u |
0.25 u |
|
Lotus paste sandwiches |
Chocolate sandwiches |
Curry sandwiches |
Total sandwiches |
Before |
1 u |
0.75 u |
0.25 u |
2 u |
Change |
- 0.8 u |
- 0.55 u |
- 0.25 u |
|
After |
0.2 u |
0.2 u |
0 |
0.4 u |
50% =
50100 =
1280% =
80100 =
45 Total number of sandwiches = 2 u
Number of chocolate and curry sandwiches
= 2 u - 1 u
= 1 u
Number of chocolate sandwiches at first
=
34 x 1 u
= 0.75 u
Number of curry sandwiches at first
= 1 u - 0.75 u
= 0.25 u
Number of lotus paste sandwiches sold
= 80% x 1 u
=
80100 x 1 u
=
45 x 1 u
= 0.8 u
Number of curry sandwiches sold
=
14 x 1 u
= 0.25 u
Number of lotus paste sandwiches left
= 1 u - 0.8 u
= 0.2 u
To maintain the percentage of the lotus paste sandwiches in the end,
50% → 0.2 u
100% →
0.250 x 100 = 0.4 u
Total number of sandwiches in the end to maintain the original percentage of lotus paste sandwiches = 0.4 u
Number of chocolate sandwiches left
= 0.4 u - 0.2 u
= 0.2 u
Number of chocolate sandwiches that Fanny must sell to maintain the original percentage of lotus paste sandwiches
= 0.75 u - 0.2 u
= 0.55 u
Percentage of the chocolate sandwiches that Fanny must sell
=
0.550.75 x 100%
= 73.3%
Answer(s): 73.3%