Olivia made sandwiches for sale. 60% of the sandwiches were lotus paste sandwiches and the rest were sardine and chocolate sandwiches in the ratio 3 : 2. If a customer bought 65% of the lotus paste sandwiches and all of the chocolate sandwiches, what percentage of the sardine sandwiches must Olivia sell for her to maintain the original percentage of lotus paste sandwiches at first? Leave your answer in decimals and correct to 1 decimal place.

Lotus paste sandwiches	Sardine sandwiches	Chocolate sandwiches
3 u	2 u
	1.2 u	0.8 u

	Lotus paste sandwiches	Sardine sandwiches	Chocolate sandwiches	Total sandwiches
Before	3 u	1.2 u	0.8 u	5 u
Change	- 1.95 u	- 0.5 u	- 0.8 u
After	1.05 u	0.7 u	0	1.75 u

60% = ⁶⁰₁₀₀ = ³₅
65% = ⁶⁵₁₀₀ = ¹³₂₀

Total number of sandwiches = 5 u

Number of sardine and chocolate sandwiches
= 5 u - 3 u
= 2 u

Number of sardine sandwiches at first
= ³₅ x 2 u
= 1.2 u

Number of chocolate sandwiches at first
= 2 u - 1.2 u
= 0.8 u

Number of lotus paste sandwiches sold
= 65% x 3 u
= ⁶⁵₁₀₀ x 3 u
= ¹³₂₀ x 3 u
= 1.95 u

Number of chocolate sandwiches sold
= ²₅ x 2 u
= 0.8 u

Number of lotus paste sandwiches left 
= 3 u - 1.95 u
= 1.05 u

To maintain the percentage of the lotus paste sandwiches in the end, 
60% → 1.05 u
100% → ^1.05₆₀ x 100 = 1.75 u

Total number of sandwiches in the end to maintain the original percentage of lotus paste sandwiches = 1.75 u

Number of sardine sandwiches left
= 1.75 u - 1.05 u
= 0.7 u

Number of sardine sandwiches that Olivia must sell to maintain the original percentage of lotus paste sandwiches
= 1.2 u - 0.7 u
= 0.5 u

Percentage of the sardine sandwiches that Olivia must sell
= ^0.5_1.2 x 100%
= 41.7%

Answer(s): 41.7%