Marion made sandwiches for sale. 45% of the sandwiches were sardine sandwiches and the rest were chocolate and egg sandwiches in the ratio 3 : 2. If a customer bought 80% of the sardine sandwiches and all of the egg sandwiches, what percentage of the chocolate sandwiches must Marion 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 |
Chocolate sandwiches |
Egg sandwiches |
9 u |
11 u |
|
6.6 u |
4.4 u |
|
Sardine sandwiches |
Chocolate sandwiches |
Egg sandwiches |
Total sandwiches |
Before |
9 u |
6.6 u |
4.4 u |
20 u |
Change |
- 7.2 u |
- 4.4 u |
- 4.4 u |
|
After |
1.8 u |
2.2 u |
0 |
4 u |
45% =
45100 =
92080% =
80100 =
45 Total number of sandwiches = 20 u
Number of chocolate and egg sandwiches
= 20 u - 9 u
= 11 u
Number of chocolate sandwiches at first
=
35 x 11 u
= 6.6 u
Number of egg sandwiches at first
= 11 u - 6.6 u
= 4.4 u
Number of sardine sandwiches sold
= 80% x 9 u
=
80100 x 9 u
=
45 x 9 u
= 7.2 u
Number of egg sandwiches sold
=
25 x 11 u
= 4.4 u
Number of sardine sandwiches left
= 9 u - 7.2 u
= 1.8 u
To maintain the percentage of the sardine sandwiches in the end,
45% → 1.8 u
100% →
1.845 x 100 = 4 u
Total number of sandwiches in the end to maintain the original percentage of sardine sandwiches = 4 u
Number of chocolate sandwiches left
= 4 u - 1.8 u
= 2.2 u
Number of chocolate sandwiches that Marion must sell to maintain the original percentage of sardine sandwiches
= 6.6 u - 2.2 u
= 4.4 u
Percentage of the chocolate sandwiches that Marion must sell
=
4.46.6 x 100%
= 66.7%
Answer(s): 66.7%