Joelle made sandwiches for sale. 45% of the sandwiches were chicken sandwiches and the rest were lotus paste and sardine sandwiches in the ratio 3 : 2. If a customer bought 75% of the chicken sandwiches and all of the sardine sandwiches, what percentage of the lotus paste sandwiches must Joelle sell for her to maintain the original percentage of chicken sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.
Chicken sandwiches |
Lotus paste sandwiches |
Sardine sandwiches |
9 u |
11 u |
|
6.6 u |
4.4 u |
|
Chicken sandwiches |
Lotus paste sandwiches |
Sardine sandwiches |
Total sandwiches |
Before |
9 u |
6.6 u |
4.4 u |
20 u |
Change |
- 6.75 u |
- 3.85 u |
- 4.4 u |
|
After |
2.25 u |
2.75 u |
0 |
5 u |
45% =
45100 =
92075% =
75100 =
34 Total number of sandwiches = 20 u
Number of lotus paste and sardine sandwiches
= 20 u - 9 u
= 11 u
Number of lotus paste sandwiches at first
=
35 x 11 u
= 6.6 u
Number of sardine sandwiches at first
= 11 u - 6.6 u
= 4.4 u
Number of chicken sandwiches sold
= 75% x 9 u
=
75100 x 9 u
=
34 x 9 u
= 6.75 u
Number of sardine sandwiches sold
=
25 x 11 u
= 4.4 u
Number of chicken sandwiches left
= 9 u - 6.75 u
= 2.25 u
To maintain the percentage of the chicken sandwiches in the end,
45% → 2.25 u
100% →
2.2545 x 100 = 5 u
Total number of sandwiches in the end to maintain the original percentage of chicken sandwiches = 5 u
Number of lotus paste sandwiches left
= 5 u - 2.25 u
= 2.75 u
Number of lotus paste sandwiches that Joelle must sell to maintain the original percentage of chicken sandwiches
= 6.6 u - 2.75 u
= 3.85 u
Percentage of the lotus paste sandwiches that Joelle must sell
=
3.856.6 x 100%
= 58.3%
Answer(s): 58.3%