Linda made sandwiches for sale. 55% of the sandwiches were curry sandwiches and the rest were chocolate and mushroom sandwiches in the ratio 3 : 2. If a customer bought 65% of the curry sandwiches and all of the mushroom sandwiches, what percentage of the chocolate sandwiches must Linda sell for her to maintain the original percentage of curry sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.
Curry sandwiches |
Chocolate sandwiches |
Mushroom sandwiches |
11 u |
9 u |
|
5.4 u |
3.6 u |
|
Curry sandwiches |
Chocolate sandwiches |
Mushroom sandwiches |
Total sandwiches |
Before |
11 u |
5.4 u |
3.6 u |
20 u |
Change |
- 7.15 u |
- 2.25 u |
- 3.6 u |
|
After |
3.85 u |
3.15 u |
0 |
7 u |
55% =
55100 =
112065% =
65100 =
1320 Total number of sandwiches = 20 u
Number of chocolate and mushroom sandwiches
= 20 u - 11 u
= 9 u
Number of chocolate sandwiches at first
=
35 x 9 u
= 5.4 u
Number of mushroom sandwiches at first
= 9 u - 5.4 u
= 3.6 u
Number of curry sandwiches sold
= 65% x 11 u
=
65100 x 11 u
=
1320 x 11 u
= 7.15 u
Number of mushroom sandwiches sold
=
25 x 9 u
= 3.6 u
Number of curry sandwiches left
= 11 u - 7.15 u
= 3.85 u
To maintain the percentage of the curry sandwiches in the end,
55% → 3.85 u
100% →
3.8555 x 100 = 7 u
Total number of sandwiches in the end to maintain the original percentage of curry sandwiches = 7 u
Number of chocolate sandwiches left
= 7 u - 3.85 u
= 3.15 u
Number of chocolate sandwiches that Linda must sell to maintain the original percentage of curry sandwiches
= 5.4 u - 3.15 u
= 2.25 u
Percentage of the chocolate sandwiches that Linda must sell
=
2.255.4 x 100%
= 41.7%
Answer(s): 41.7%