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

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.