Xylia made sandwiches for sale. 60% of the sandwiches were sardine sandwiches and the rest were lotus paste and curry sandwiches in the ratio 3 : 2. If a customer bought 60% of the sardine sandwiches and all of the curry sandwiches, what percentage of the lotus paste sandwiches must Xylia sell for her to maintain the original percentage of sardine sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.
Sardine sandwiches |
Lotus paste sandwiches |
Curry sandwiches |
3 u |
2 u |
|
1.2 u |
0.8 u |
|
Sardine sandwiches |
Lotus paste sandwiches |
Curry sandwiches |
Total sandwiches |
Before |
3 u |
1.2 u |
0.8 u |
5 u |
Change |
- 1.8 u |
- 0.4 u |
- 0.8 u |
|
After |
1.2 u |
0.8 u |
0 |
2 u |
60% =
60100 =
3560% =
60100 =
35 Total number of sandwiches = 5 u
Number of lotus paste and curry sandwiches
= 5 u - 3 u
= 2 u
Number of lotus paste sandwiches at first
=
35 x 2 u
= 1.2 u
Number of curry sandwiches at first
= 2 u - 1.2 u
= 0.8 u
Number of sardine sandwiches sold
= 60% x 3 u
=
60100 x 3 u
=
35 x 3 u
= 1.8 u
Number of curry sandwiches sold
=
25 x 2 u
= 0.8 u
Number of sardine sandwiches left
= 3 u - 1.8 u
= 1.2 u
To maintain the percentage of the sardine sandwiches in the end,
60% → 1.2 u
100% →
1.260 x 100 = 2 u
Total number of sandwiches in the end to maintain the original percentage of sardine sandwiches = 2 u
Number of lotus paste sandwiches left
= 2 u - 1.2 u
= 0.8 u
Number of lotus paste sandwiches that Xylia must sell to maintain the original percentage of sardine sandwiches
= 1.2 u - 0.8 u
= 0.4 u
Percentage of the lotus paste sandwiches that Xylia must sell
=
0.41.2 x 100%
= 33.3%
Answer(s): 33.3%