Alex bought 144 bagels for $80. His profit was $75 once he had sold 100 bagels. Which equation represents Alex's profit,P as a function of the number sold, n?
Cost of the bagels is 144 for $80.
When he sold 100 bagels, he has earned $155 gross (which is his profit of $75 + cost of $80).
Therefore 1 bagel is sold for $1.55.
He earns $1.55n
but since his costs are $80,
P=1.55n - 80
ok, thank you! But i don't understand why you need to find the gross?
wait... isnt gross the revenue? lol sorry if that's a dumb query
Well, it seems like Alex is quite the bagel entrepreneur. Let's break down the problem at hand. Alex bought 144 bagels for $80, and his profit was $75 once he sold 100 bagels.
To find an equation that represents Alex's profit P as a function of the number sold n, we can start by figuring out how much each bagel costs Alex. He bought 144 bagels for $80, which means each bagel cost him $80/144 = $0.5556 (rounded to four decimal places).
Now, let's focus on the profit. Once Alex sold 100 bagels, he earned a profit of $75. Let's figure out how much profit he makes per bagel sold. The profit per bagel can be calculated by dividing the total profit by the number of bagels sold. Thus, the profit per bagel is $75/100 = $0.75.
The equation representing Alex's profit P as a function of the number sold n can now be formed. Let's give it a whirl:
P(n) = (0.75n) - (0.5556n)
This equation takes into account the profit per bagel sold (0.75n) and the cost per bagel (0.5556n) to calculate the overall profit as a function of the number of bagels sold.
Keep in mind that this equation assumes a linear relationship between profits and the number of bagels sold. It's like bamboozling math with a side of bagel humor.
To find the equation that represents Alex's profit as a function of the number of bagels sold, we can break down the given information into mathematical expressions.
Let's represent the profit as "P" and the number of bagels sold as "n."
From the given information, we know that Alex bought 144 bagels for $80. This means that the cost price of each bagel is $80/144.
To determine Alex's profit, we need to subtract the cost price from the selling price. Since the profit is $75 after selling 100 bagels, we can calculate the selling price per bagel using the formula:
Selling Price = Cost Price + Profit
Selling Price = $80/144 + $75/100
Now, we can express the profit as a function of the number of bagels sold:
P(n) = (Selling Price - Cost Price) × number of bagels sold
P(n) = [(80/144 + 75/100) - (80/144)] × n
Simplifying further:
P(n) = [(80/144 + 75/100) - (80/144)] × n
P(n) = [(20/36 + 54/36) - 20/36] × n
P(n) = (74/36) × n
P(n) = (37/18) × n
Therefore, the equation that represents Alex's profit (P) as a function of the number of bagels sold (n) is:
P(n) = (37/18) × n