A merchant purchased a number of coats, each at the same price, for a total of $720. He sold them at $40 each, thus realizing a profit equal to his cost of 8 coats. How many did he buy

number of coats --- n

purchase cost per coat = 720/n

total return = 40n
profit = 40n - 720

cost of 8 coats = 8(720/n)

40n - 720 = 8(720/n)
40n^2 - 720n - 5760 = 0
n2 - 18n - 144 = 0
(n - 24)(n + 6) = 0
n = 24 or n=-6, rejecting the negative

He bought 24 coats

check:
cost per coat = 720/24 = $30
cost of 8 coats = $240

profit on each coat = $10
total profit = 24(10) = $240
My answer is correct

Well, it seems like this merchant was trying to engage in some coat-tastic business! Let's solve this puzzle while keeping a fun-loving spirit.

If the merchant bought n coats, and each coat had the same price, then the cost of each coat would be 720 / n dollars.

Now, let's see what happens when the merchant sells these coats at $40 each. The total selling price would be 40n dollars.

We are told that the merchant made a profit equal to the cost of 8 coats. So, the profit earned would be 720 / n * 8 dollars.

Since the profit made is equal to the cost of 8 coats, we can equate the two expressions:

720 / n * 8 = 720

Now, let's have some fun with algebra and solve this equation:

8 * 720 = 720 * n

5760 = 720 * n

Dividing both sides by 720:

5760 / 720 = n

8 = n

Ta-da! Looks like our merry merchant bought 8 coats. Nothing like a little coat-counting comedy to brighten up the day!

Let's break down the information given step-by-step:

1. Let's assume that the merchant bought "x" coats.

2. The total cost of "x" coats would be the price per coat multiplied by the number of coats, which is equal to $720. Therefore, the price per coat can be calculated as $720 divided by "x".

3. The merchant sold each coat for $40. So, the total revenue from selling "x" coats would be $40 multiplied by "x".

4. The profit is equal to the revenue minus the cost. According to the information given, the profit is equal to the cost of 8 coats. Therefore, the profit can be calculated as the price per coat multiplied by 8.

Now, let's put these steps together to form an equation:

Revenue - Cost = Profit

($40 * x) - ($720 / x) = ($720 / x) * 8

Now, we can simplify and solve the equation:

40x - 720/x = 8 * 720/x

Multiply both sides by "x" to eliminate the denominators:

40x^2 - 720 = 8 * 720

Simplify:

40x^2 - 720 = 5760

Rearrange the equation:

40x^2 = 6480

Divide both sides by 40:

x^2 = 162

Take the square root of both sides:

x = sqrt(162)

x ≈ 12.73

Since the merchant cannot buy a fraction of a coat, we need to round down the decimal to the nearest whole number.

Therefore, the merchant bought approximately 12 coats.

To determine the number of coats the merchant bought, we need to set up an equation based on the given information.

Let's assume the merchant bought x coats. Since each coat was purchased at the same price, let's represent the cost of each coat as c.

According to the given information, the total cost of all the coats is $720. Therefore, we can write the equation:

Total Cost = Number of Coats * Cost per Coat
720 = x * c

Next, we know that the merchant sold each coat for $40, which resulted in a profit equal to the cost of 8 coats. This can be expressed as:

Profit = Selling Price per Coat - Cost per Coat
8c = 40 - c

Now, we have a system of two equations:

720 = xc
8c = 40 - c

We can solve this system of equations to find the values of x and c.

First, let's solve the second equation for c:

8c + c = 40
9c = 40
c = 40/9

Now, substitute the value of c into the first equation to find x:

720 = x * (40/9)
720 = 40x/9

To solve for x, we can cross-multiply:

(40/9) * x = 720
40x = 720 * 9
40x = 6480
x = 6480/40
x = 162

Therefore, the merchant bought 162 coats.