Vanessa made buns for sale. 55% of the buns were egg buns and the rest were mushroom and beef buns in the ratio 3 : 2. If a customer bought 65% of the egg buns and all of the beef buns, what percentage of the mushroom buns must Vanessa sell for her to maintain the original percentage of egg buns at first? Leave your answer in decimals and correct to 1 decimal place.

Egg buns	Mushroom buns	Beef buns
11 u	9 u
	5.4 u	3.6 u

	Egg buns	Mushroom buns	Beef buns	Total buns
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 = ¹¹₂₀
65% = ⁶⁵₁₀₀ = ¹³₂₀

Total number of buns = 20 u

Number of mushroom and beef buns
= 20 u - 11 u
= 9 u

Number of mushroom buns at first
= ³₅ x 9 u
= 5.4 u

Number of beef buns at first
= 9 u - 5.4 u
= 3.6 u

Number of egg buns sold
= 65% x 11 u
= ⁶⁵₁₀₀ x 11 u
= ¹³₂₀ x 11 u
= 7.15 u

Number of beef buns sold
= ²₅ x 9 u
= 3.6 u

Number of egg buns left 
= 11 u - 7.15 u
= 3.85 u

To maintain the percentage of the egg buns in the end, 
55% → 3.85 u
100% → ^3.85₅₅ x 100 = 7 u

Total number of buns in the end to maintain the original percentage of egg buns = 7 u

Number of mushroom buns left
= 7 u - 3.85 u
= 3.15 u

Number of mushroom buns that Vanessa must sell to maintain the original percentage of egg buns
= 5.4 u - 3.15 u
= 2.25 u

Percentage of the mushroom buns that Vanessa must sell
= ^2.25_5.4 x 100%
= 41.7%

Answer(s): 41.7%