Natalie made sandwiches for sale. 50% of the sandwiches were chocolate sandwiches and the rest were egg and chicken sandwiches in the ratio 3 : 2. If a customer bought 80% of the chocolate sandwiches and all of the chicken sandwiches, what percentage of the egg sandwiches must Natalie sell for her to maintain the original percentage of chocolate sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.

Chocolate sandwiches	Egg sandwiches	Chicken sandwiches
1 u	1 u
	0.6 u	0.4 u

	Chocolate sandwiches	Egg sandwiches	Chicken sandwiches	Total sandwiches
Before	1 u	0.6 u	0.4 u	2 u
Change	- 0.8 u	- 0.4 u	- 0.4 u
After	0.2 u	0.2 u	0	0.4 u

50% = ⁵⁰₁₀₀ = ¹₂
80% = ⁸⁰₁₀₀ = ⁴₅

Total number of sandwiches = 2 u

Number of egg and chicken sandwiches
= 2 u - 1 u
= 1 u

Number of egg sandwiches at first
= ³₅ x 1 u
= 0.6 u

Number of chicken sandwiches at first
= 1 u - 0.6 u
= 0.4 u

Number of chocolate sandwiches sold
= 80% x 1 u
= ⁸⁰₁₀₀ x 1 u
= ⁴₅ x 1 u
= 0.8 u

Number of chicken sandwiches sold
= ²₅ x 1 u
= 0.4 u

Number of chocolate sandwiches left 
= 1 u - 0.8 u
= 0.2 u

To maintain the percentage of the chocolate 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 chocolate sandwiches = 0.4 u

Number of egg sandwiches left
= 0.4 u - 0.2 u
= 0.2 u

Number of egg sandwiches that Natalie must sell to maintain the original percentage of chocolate sandwiches
= 0.6 u - 0.2 u
= 0.4 u

Percentage of the egg sandwiches that Natalie must sell
= ^0.4_0.6 x 100%
= 66.7%

Answer(s): 66.7%