Fiona made sandwiches for sale. 50% of the sandwiches were chicken sandwiches and the rest were beef and mushroom sandwiches in the ratio 3 : 2. If a customer bought 65% of the chicken sandwiches and all of the mushroom sandwiches, what percentage of the beef sandwiches must Fiona 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	Beef sandwiches	Mushroom sandwiches
1 u	1 u
	0.6 u	0.4 u

	Chicken sandwiches	Beef sandwiches	Mushroom sandwiches	Total sandwiches
Before	1 u	0.6 u	0.4 u	2 u
Change	- 0.65 u	- 0.25 u	- 0.4 u
After	0.35 u	0.35 u	0	0.7 u

50% = ⁵⁰₁₀₀ = ¹₂
65% = ⁶⁵₁₀₀ = ¹³₂₀

Total number of sandwiches = 2 u

Number of beef and mushroom sandwiches
= 2 u - 1 u
= 1 u

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

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

Number of chicken sandwiches sold
= 65% x 1 u
= ⁶⁵₁₀₀ x 1 u
= ¹³₂₀ x 1 u
= 0.65 u

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

Number of chicken sandwiches left 
= 1 u - 0.65 u
= 0.35 u

To maintain the percentage of the chicken sandwiches in the end, 
50% → 0.35 u
100% → ^0.35₅₀ x 100 = 0.7 u

Total number of sandwiches in the end to maintain the original percentage of chicken sandwiches = 0.7 u

Number of beef sandwiches left
= 0.7 u - 0.35 u
= 0.35 u

Number of beef sandwiches that Fiona must sell to maintain the original percentage of chicken sandwiches
= 0.6 u - 0.35 u
= 0.25 u

Percentage of the beef sandwiches that Fiona must sell
= ^0.25_0.6 x 100%
= 41.7%

Answer(s): 41.7%