Aco is running a lemonade stand to raise money for his school’s charity event. He sells small cups of lemonade for $1.50 each and large cups for $2.75 each. On the first day, he sold a total of 35 cups of lemonade, making a total of $71.25 in sales. If he sold twice as many small cups as large cups, how many of each size did he sell?
Let's say Aco sold x small cups of lemonade.
Since he sold twice as many small cups as large cups, he sold a total of 2x large cups.
He sold x small cups for $1.50 each, making a total of 1.50*x = $<<1.5*x=1.5x>>1.5x in sales.
He also sold 2x large cups for $2.75 each, making a total of 2.75*2*x = $<<2.75*2*x=5.5x>>5.5x in sales.
The total number of cups he sold is x+2x = 3x.
The total sales from the small cups and large cups are 1.5x + 5.5x = 7x.
Since the total sales for the cups sold is $71.25, this means 7x = 71.25
The average price per cup of lemonade is $71.25 / 35 = $<<71.25/35=2.0357142857142856>>2.04/cup
Dividing the total sales by the average price per cup gives 7x = $71.25 / $2.04/cup = 35
7x = 35
x = 35 / 7 = <<35/7=5>>5
Aco sold 5 small cups of lemonade for a total of 5 * $1.50 = $<<5*1.5=7.50>>7.50
He sold 2 * 5 = <<2*5=10>>10 large cups for a total of 10 * $2.75 = $<<2.75*10=27.50>>27.50
In total, he sold 5 + 10 = <<5+10=15>>15 cups of lemonade. Answer: \boxed{5,10}.