A bicycle store costs $4200 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $180. How many bicycles must the store sell each month to break even?

Question

A bicycle store costs $4200 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $180. How many bicycles must the store sell each month to break even?

The store must sell ___ bicycles each month to break even.

Answer 1

To break even, the store's total revenue must equal its total expenses. Let x be the number of bicycles sold each month. Then, the total revenue is:

Revenue = Selling price per bike x Number of bikes sold
Revenue = $180 x x
Revenue = $180x

The total expenses are the fixed cost plus the variable cost of producing the bikes:

Expenses = Fixed cost + Variable cost per bike x Number of bikes sold
Expenses = $4200 + $40x

To break even, we set the revenue equal to the expenses and solve for x:

$180x = $4200 + $40x
$140x = $4200
x = 30

Therefore, the store must sell 30 bicycles each month to break even.

Answer 2

An investor invested a total of $2,000 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $94, how much was invested in each mutual fund?

The amount invested in the mutual fund that earned 6% was $___.

The amount invested in the mutual fund that earned 4% was $___.

Answer 3

Let x be the amount invested in the mutual fund that earned 6% and y be the amount invested in the mutual fund that earned 4%. We have two equations based on the given information:

x + y = 2000 (equation 1)
0.06x + 0.04y = 94 (equation 2)

We can use equation 1 to come up with an expression for y in terms of x:

y = 2000 - x

Substituting this expression into equation 2, we get:

0.06x + 0.04(2000-x) = 94

Simplifying this equation, we get:

0.02x + 80 = 94
0.02x = 14
x = 700

So the amount invested in the mutual fund that earned 6% was $700. Using equation 1, we can find that the amount invested in the mutual fund that earned 4% was:

y = 2000 - x
y = 2000 - 700
y = 1300

Therefore, the amount invested in the mutual fund that earned 4% was $1300.

Answer 4

To find the number of bicycles the store must sell each month to break even, we need to find the total cost and the total revenue.

Let's start with the total cost:
The store costs $4200 per month to operate.

Now let's find the total revenue:
The store sells each bicycle for an average price of $180.

Let's calculate the break-even point:

Total cost = Total revenue

$4200 = ($40 x Number of bicycles sold)

Number of bicycles sold = Total cost / $40

Number of bicycles sold = $4200 / $40

Number of bicycles sold = 105

So, the store must sell 105 bicycles each month to break even.

A bicycle store costs ​$4200 per month to operate. The store pays an average of ​$40 per bike. The average selling price of each bicycle is ​$180. How many bicycles must the store sell each month to break​ even?

To break even, the store's total revenue must equal its total expenses. Let x be the number of bicycles sold each month. Then, the total revenue is:

An investor invested a total of $2,000 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $94, how much was invested in each mutual fund?

Let x be the amount invested in the mutual fund that earned 6% and y be the amount invested in the mutual fund that earned 4%. We have two equations based on the given information:

To find the number of bicycles the store must sell each month to break even, we need to find the total cost and the total revenue.

A bicycle store costs $4200 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $180. How many bicycles must the store sell each month to break even?