Answer: You receive 14x+45 dollars for each gallon of cider that you sell.
Step-by-step explanation:
Given: For selling each gallon of cider, the company receives x dollars.
You receive = Remaining amount
i.e. You receive $(Selling price - x)
By selling 15 gallons in 15x+45 dollars, you have received (15x+45)-x dollars
i.e. You received 15x+45-x dollars
i.e. You received 14x+45 dollars.
Hence, you receive 14x+45 dollars for each gallon of cider that you sell.
1+2=21, 2+3=36, 3+4=43, 4+5=52.
Let x be the width of the cardboard (which means the length of the cardboard is x+88), then the dimensions of the box are:
Length = [(x + 88) - 2(33)]
Width = x - 2(33)
Heighth = 33
Volume = length · width · heighth
144,144 = [(x + 88) - 2(33)] · [x - 2(33)] · 33
144,144 = (x+22)(x-66)(33)
4368 = (x+22)(x-66)
4368 = x² - 44x - 1452
0 = x² - 44x - 5820
use the quadratic formula to calculate that x = 101
Answer: cardboard width = 101, cardboard length = 189
