a retailer planned to buy some computers from a total of sh 1,800,000. before the retailer could buy the computers the price per unit was reduced by sh 4000. this reduction in price enabled the retailer to buy 5 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 15 percent profit. calculate the profit made by thf retailer on each computer sold.
If the original price was p and he could get c computers, then
p*c = 180000
At the reduced price,
(p-400)(c+5) = 180000
(180000/c - 400)(c+5) = 180000
c = 45
Now you should be able to answer the questions.
To find the number of computers the retailer bought, we can use the information that the price per unit was reduced by sh 4000 and the same amount of money was used to buy 5 more computers.
Let's assume the original price per unit was X.
(a) The price per unit after the reduction is X - 4000.
Since the same amount of money was used to buy 5 more computers, we can set up the equation:
(X - 4000) * (original number of computers + 5) = X * original number of computers
To solve for the original number of computers, we can simplify the equation:
(X - 4000) * (original number of computers + 5) = X * original number of computers
X * original number of computers + 5X - 4000 * original number of computers - 5 * 4000 = X * original number of computers
5X - 4000 * original number of computers - 5 * 4000 = 0
5X - 4000 * original number of computers = 5 * 4000
5X - 4000 * original number of computers = 20000
Simplifying further:
5X = 20000 + 4000 * original number of computers
5X - 4000 * original number of computers = 20000
We don't have enough information to determine the exact values of X and the original number of computers, so we can't solve for them explicitly. However, you can substitute different values for X and solve for the original number of computers.
(b) To calculate the profit made by the retailer on each computer sold, we first need to determine the selling price per unit.
Let's assume the selling price per unit is Y.
The retailer made a 15 percent profit, so the selling price per unit is 115% of the original price per unit:
Y = 1.15X
The profit made on each computer sold is the selling price per unit (Y) minus the original price per unit (X):
Profit per computer = Y - X
Profit per computer = 1.15X - X
Profit per computer = 0.15X
Therefore, the profit made by the retailer on each computer sold is 0.15 times the original price per unit.
To determine the number of computers the retailer bought and the profit made on each computer sold, we can follow these steps systematically:
(a) Determine the number of computers the retailer bought:
1. Calculate the initial price per unit before the reduction:
Let's assume the original price per unit is P. Since the total amount of money planned for the purchase is specified as sh 1,800,000, we can write the equation:
P x Total Number of Computers = sh 1,800,000.
2. Calculate the price per unit after the reduction:
The price per unit was reduced by sh 4000, so the new price per unit becomes (P - 4000).
3. Determine the number of computers the retailer could buy with the reduced price:
Since it was mentioned that the reduced price allowed the retailer to buy 5 more computers, we can write the equation:
(P - 4000) x (Total Number of Computers + 5) = sh 1,800,000.
4. Solve the equations:
Now, we have two equations with two unknowns. We can solve them simultaneously to find the values. Simplifying the equations gives us:
(P) * (Total Number of Computers) = sh 1,800,000
(P - 4000) * (Total Number of Computers + 5) = sh 1,800,000
From equation (1), we can express Total Number of Computers in terms of P:
Total Number of Computers = sh 1,800,000 / P
Substituting this value into equation (2):
(P - 4000) * ((sh 1,800,000 / P) + 5) = sh 1,800,000
Simplifying the equation further gives us:
(P - 4000) * (P + 5) = P
Expanding and rearranging terms gives:
P^2 + 5P - 4000P - 20,000 = P
P^2 - 3995P - 20,000 = 0
We can now solve this quadratic equation using the quadratic formula:
Considering the general form of a quadratic equation as ax^2 + bx + c = 0,
a = 1, b = -3995, c = -20000
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / 2a
Using the quadratic formula, we can determine the two possible values for P (the original price per unit). Select the positive value since a price cannot be negative.
Solving the equation gives:
P ≈ 6039.545 or P ≈ 3295.45
Now, substitute P = 6039.545 back into equation (1) to find the Total Number of Computers:
Total Number of Computers = sh 1,800,000 / 6039.545
Total Number of Computers ≈ 297.96
Since we cannot have a fractional number of computers, we will round it down to the nearest whole number:
Total Number of Computers = 297
Therefore, the retailer bought 297 computers.
(b) Calculate the profit made on each computer sold:
1. Determine the selling price per computer:
As the retailer made a 15% profit on each computer, we need to calculate the selling price per computer.
Let's assume the cost price (original price per unit) is C.
Selling price = Cost price + Profit
Selling price = C + 15% of C
Selling price = C + (15/100) * C
Selling price = C(1 + 0.15)
Selling price = 1.15 * C
2. Calculate the total profit made by the retailer:
Since the retailer sold all the computers except the two damaged ones, the total profit made can be calculated using the formula: Profit = (Selling Price - Original Price) * Number of Computers Sold
Total Profit = (1.15C - C) * (297 - 2)
3. Calculate the profit made on each computer sold:
Profit per computer = Total Profit / Number of Computers Sold
Substituting the values, we can calculate the profit per computer sold.
Please note that the exact values of C and the profit per computer cannot be determined without additional information.