A stall was selling flowers. ¹₅ of the earnings are from the sale of 11 roses and 17 orchids. Of the rest of the earnings, ²₃ are from the sale of roses and ¹₃ are from the sale of orchids. Each orchid costs twice as much as each rose. How many flowers were sold?

11 roses and 17 orchids	Rest of the earnings		Total earnings
1x3	4x3
	Roses	Carnations
	2x4	1x4
3	8	4	15

Fraction of the earnings left after the sale of 11 roses and 17 orchids
= 1 - ¹₅
= ⁴₅ 

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

Cost of 1 rose = 1 u
Cost of 1 orchid = 2 u

Cost of 11 roses = 11 x 1 u = 11 u
Cost of 17 orchids = 17 x 2 u = 34 u

Total cost of 11 roses and 17 orchids
= 11 u + 34 u
= 45 u

³₁₅ of the earnings → 45 u 
¹₁₅ of the earnings → 45 u ÷ 3 = 15 u 

⁸₁₅ of the earnings → 8 x 15 u = 120 u 

Number of roses sold that contributed to the rest of the earnings
= 120 u ÷ 1 u
= 120

⁴₁₅ of the earnings → 4 x 15 u = 60 u

Number of orchids sold that contributed to the rest of the earnings
= 60 u ÷ 2 u
= 30

Number of flowers sold
= 11 + 17 + 120 + 30
= 178

Answer(s): 178