A retailer planned to buy some computers form a wholesaler for a total of shilling 1,800,000. Before the retailer could buy the computers the price per unit was reduced by shilling 4,000. This reduction in price enabled the retailer to buy five more computers using the same amount of money as originally planned.

(a) Determine the number of computers the retailer bought;
(b) Two of the computers purchased got damaged while in store, the rest were sold and the retailer made a 1 5% profit. Calculate the profit made by the retailer on each computer sold.

If the price was p, then

1800000/(p-4000) = 1800000/p +5
p = 40000
so, at $4000 each he could buy 45
at 3600 each, he could buy 50

he sold 48 computers for 1800000 * 1.15
. . .

(a) Well, it seems like the retailer got a good deal with that price reduction! Let's do some math to find out how many computers they ended up buying.

Let's assume the original price per computer was x shillings. If the total cost of the computers was 1,800,000 shillings, we can write the equation:

x * n = 1,800,000,

where n is the number of computers the retailer originally planned to buy.

Now, after the price reduction of 4,000 shillings per unit, the new price per computer is (x - 4,000) shillings. The retailer was able to buy 5 more computers with the same amount of money, so we can write another equation:

(x - 4,000) * (n + 5) = 1,800,000.

Now we have a system of equations:

x * n = 1,800,000,
(x - 4,000) * (n + 5) = 1,800,000.

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

Solving the first equation for x, we get:

x = 1,800,000 / n.

Substitute this value of x into the second equation:

(1,800,000 / n - 4,000) * (n + 5) = 1,800,000.

Multiplying out the brackets and simplifying, we have:

(1,800,000 - 4,000n) * (n + 5) = 1,800,000.

Expanding further:

1,800,000n + 9,000,000 - 4,000n^2 - 20,000n = 1,800,000.

Rearranging and simplifying:

4,000n^2 - 9,800,000n + 9,000,000 = 0.

Dividing through by 1,000 to simplify:

4n^2 - 9,800n + 9,000 = 0.

Now we can solve this quadratic equation to find the value of n.

(b) Once we find the value of n, we can calculate the profit made by the retailer on each computer sold. But first, let's celebrate the fact that the retailer managed to buy more computers at a lower price! Kudos to them for being such a savvy shopper!

Let's solve this step-by-step:

(a) Determine the number of computers the retailer bought.

Let's assume the original price per unit of the computers is P.
Based on the given information, the total amount the retailer planned to spend is 1,800,000 shillings.
So, we can write the equation: P * N = 1,800,000, where N is the number of computers initially planned to buy.

After the price was reduced by 4,000 shillings per unit, the new price per unit is P - 4,000.
The retailer was able to buy five more computers using the same amount of money. Therefore, we can write the equation: (P - 4,000) * (N + 5) = 1,800,000.

Now, we can solve these two equations simultaneously to find the values of P and N.

From the first equation, rearrange it to get P = 1,800,000 / N.

Substitute this value of P in the second equation:

(1,800,000 / N) - 4,000 = (1,800,000 / (N + 5))

Multiply both sides of the equation by N(N + 5) to eliminate the denominators:

1,800,000(N + 5) - 4,000N(N + 5) = 1,800,000N

Expand and simplify the equation:

1,800,000N + 9,000,000 - 4,000N^2 - 20,000N = 1,800,000N

Rearrange the equation to form a quadratic equation:

4,000N^2 + 21,800N - 9,000,000 = 0

Now we can solve this quadratic equation for N.

To find the number of computers the retailer bought, we need to solve the problem step by step.

(a) Let's assume the original price per computer was x shillings. So, the original plan was to buy 1,800,000 / x computers.

But after the price reduction of 4,000 shillings per computer, the new price per computer is (x - 4,000) shillings.

Now, the retailer can buy 5 more computers than the original plan with the same total amount of money, i.e. (1,800,000 / x) + 5 computers.

Since the total amount of money spent remains the same, we can set up the following equation:
1,800,000 / x = [(1,800,000 / x) + 5] * (x - 4,000)

To solve this equation, we can multiply both sides by x to eliminate the denominators:

1,800,000 = (1,800,000 + 5x) * (x - 4,000)

Next, we can expand the right side of the equation:

1,800,000 = (1,800,000 * x) - (5 * 4,000 * x) - (1,800,000 * 4,000) + (5 * 4,000 * x)

Combining like terms:

1,800,000 = 1,800,000x - 20,000x - 7,200,000 + 20,000x

Simplifying:

1,800,000 = 1,800,000x - 7,200,000

Rearranging the equation:

1,800,000x = 1,800,000 + 7,200,000

1,800,000x = 9,000,000

Dividing both sides by 1,800,000:

x = 5

Therefore, the original price per computer was 5 shillings.

Substituting this value back into the equation (1,800,000 / x), we get:

1,800,000 / 5 = 360,000

So, the retailer bought a total of 360,000 computers.

(b) Now, let's calculate the profit made by the retailer on each computer sold.

The retailer made a 15% profit on each computer sold. This means the selling price per computer would be 1.15 times the original price per computer.

Profit per computer = Selling price per computer - Original price per computer
Profit per computer = (1.15 * 5) - 5
Profit per computer = (5.75) - 5
Profit per computer = 0.75 shillings

Therefore, the retailer made a profit of 0.75 shillings on each computer sold.