1. A firm pays $1.75 for each copy of a magazine and sells each one for $2.50. There is a fixed monthly cost of $40 for printing the publication. If the firm wants to make $550 dollars next month, how many magazines do they have to sell?

Question

1. A firm pays $1.75 for each copy of a magazine and sells each one for $2.50. There is a fixed monthly cost of $40 for printing the publication. If the firm wants to make $550 dollars next month, how many magazines do they have to sell?

Answer 1

oops, the $40 is a cost, not a profit

x(2.50-1.75) - 40.00 >= 550.00
x >= 754

Answer 2

For x magazines, we need

x(2.50-1.75) + 40.00 >= 550.00
x >= 680

Answer 3

To find out how many magazines the firm needs to sell in order to make $550 next month, we need to calculate the number of magazines they need to sell to cover their costs and then calculate the additional number of magazines they need to sell to reach the desired profit.

First, let's determine the number of magazines they need to sell to cover their costs:

The fixed monthly cost for printing the publication is $40.

For each magazine, the firm pays $1.75.

To find the number of magazines needed to cover the fixed monthly cost, we can use the formula:

Number of magazines = Fixed monthly cost / Cost per magazine

Number of magazines = $40 / $1.75 = 22.857 (rounded up to 23 magazines)

So, the firm needs to sell at least 23 magazines to cover their costs.

Next, let's calculate the additional number of magazines they need to sell to reach the desired profit:

Desired profit = $550

Profit per magazine = Selling price per magazine - Cost per magazine

Profit per magazine = $2.50 - $1.75 = $0.75

To find the additional number of magazines needed to reach the desired profit, we can use the formula:

Additional number of magazines = Desired profit / Profit per magazine

Additional number of magazines = $550 / $0.75 = 733.33 (rounded up to 734 magazines)

So, the firm needs to sell an additional 734 magazines to reach the desired profit.

Finally, to find the total number of magazines they need to sell, we add the number of magazines needed to cover the costs to the additional number of magazines needed to reach the desired profit:

Total number of magazines = Number of magazines to cover costs + Additional number of magazines to reach desired profit

Total number of magazines = 23 + 734 = 757 magazines

Therefore, the firm needs to sell 757 magazines to make $550 next month.