A stall was selling flowers. ¹₄ of the earnings are from the sale of 11 carnations and 15 orchids. Of the rest of the earnings, ³₄ are from the sale of carnations and ¹₄ are from the sale of orchids. Each orchid costs thrice as much as each carnation. How many flowers were sold?

11 carnations and 15 orchids	Rest of the earnings		Total earnings
1x4	3x4
	Roses	Carnations
	3x3	1x3
4	9	3	16

Fraction of the earnings left after the sale of 11 carnations and 15 orchids
= 1 - ¹₄
= ³₄ 

The rest of the earnings is repeated. LCM of 3 and 4 is 12.

Cost of 1 carnation = 1 u
Cost of 1 orchid = 3 u

Cost of 11 carnations = 11 x 1 u = 11 u
Cost of 15 orchids = 15 x 3 u = 45 u

Total cost of 11 carnations and 15 orchids
= 11 u + 45 u
= 56 u

⁴₁₆ of the earnings → 56 u 
¹₁₆ of the earnings → 56 u ÷ 4 = 14 u 

⁹₁₆ of the earnings → 9 x 14 u = 126 u 

Number of carnations sold that contributed to the rest of the earnings
= 126 u ÷ 1 u
= 126

³₁₆ of the earnings → 3 x 14 u = 42 u

Number of orchids sold that contributed to the rest of the earnings
= 42 u ÷ 3 u
= 14

Number of flowers sold
= 11 + 15 + 126 + 14
= 166

Answer(s): 166