A stall was selling flowers. ¹₆ of the earnings are from the sale of 12 roses and 13 lavenders. Of the rest of the earnings, ³₄ are from the sale of roses and ¹₄ are from the sale of lavenders. Each lavender costs four times as much as each rose. How many flowers were sold?

12 roses and 13 lavenders	Rest of the earnings		Total earnings
1x4	5x4
	Roses	Carnations
	3x5	1x5
4	15	5	24

Fraction of the earnings left after the sale of 12 roses and 13 lavenders
= 1 - ¹₆
= ⁵₆ 

The rest of the earnings is repeated. LCM of 5 and 4 is 20.

Cost of 1 rose = 1 u
Cost of 1 lavender = 4 u

Cost of 12 roses = 12 x 1 u = 12 u
Cost of 13 lavenders = 13 x 4 u = 52 u

Total cost of 12 roses and 13 lavenders
= 12 u + 52 u
= 64 u

⁴₂₄ of the earnings → 64 u 
¹₂₄ of the earnings → 64 u ÷ 4 = 16 u 

¹⁵₂₄ of the earnings → 15 x 16 u = 240 u 

Number of roses sold that contributed to the rest of the earnings
= 240 u ÷ 1 u
= 240

⁵₂₄ of the earnings → 5 x 16 u = 80 u

Number of lavenders sold that contributed to the rest of the earnings
= 80 u ÷ 4 u
= 20

Number of flowers sold
= 12 + 13 + 240 + 20
= 285

Answer(s): 285