A stall was selling flowers. ¹₅ of the earnings are from the sale of 6 lilies and 12 carnations. Of the rest of the earnings, ²₃ are from the sale of lilies and ¹₃ are from the sale of carnations. Each carnation costs four times as much as each lily. How many flowers were sold?

6 lilies and 12 carnations	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 6 lilies and 12 carnations
= 1 - ¹₅
= ⁴₅ 

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

Cost of 1 lily = 1 u
Cost of 1 carnation = 4 u

Cost of 6 lilies = 6 x 1 u = 6 u
Cost of 12 carnations = 12 x 4 u = 48 u

Total cost of 6 lilies and 12 carnations
= 6 u + 48 u
= 54 u

³₁₅ of the earnings → 54 u 
¹₁₅ of the earnings → 54 u ÷ 3 = 18 u 

⁸₁₅ of the earnings → 8 x 18 u = 144 u 

Number of lilies sold that contributed to the rest of the earnings
= 144 u ÷ 1 u
= 144

⁴₁₅ of the earnings → 4 x 18 u = 72 u

Number of carnations sold that contributed to the rest of the earnings
= 72 u ÷ 4 u
= 18

Number of flowers sold
= 6 + 12 + 144 + 18
= 180

Answer(s): 180