Question 993902
if he sold all 2900 at 8 dollars each, he would get 23200 total.


that's 550 short of his goal of at least 23750.


the difference in price between 8 and 8.50 is .50.


take the 550 and divide it by .50 and you get 1100.


he would need to sell a minimum of 1100 units at 8.50.


2900 - 1100 = 1800.


he would therefore sell 1800 at 8.00 and 1100 at 8.50 and he would get 8 * 1800 = 14,400 + 8.50 * 1100 = 9,350 for a total orf 23,750.


you can also solve this algebraically as follows:


x = number of units sold at 8 dollars each.
y = number of units sold at 8.5 dollars each.


first equation is x + y = 2900
second equation is 8x + 8.5y >= 23750


from the first equation, solve for y to get y = 2900 - x


replace y with 2900 - x in the second equation to get:


8x + 8.5 * (2900-x) >= 23750


simplify to get:


8x + 24650 - 8.5x >= 23750


subtract 8x from both sides of this equation and subtract 23750 from both sides of this equation to get:


24650 - 23750 = 8.5x - 8x


simplify to get:


900 = .5x


divide both sides of this equation by 1.5 to get:


x = 1800.


since x + y = 2900, this means that y = 1100.


solution is x = 1800 and y = 1100


x is the number sold at 8 dollars
y is the number sold at 8.5 dollars


same answer as before when we used logic.