A school planned to buy x calculators for a total cost of Ksh 16200. The supplier agreed to offer a discount of Ksh 60 per calculator. The school was the able to get three extra calculators for the same amount of money.
(a) Write an expression in terms of x, for the:
(i) Original price of each calculator;
(ii) Price of each calculator after the discount.
(b) Form an equation in x and hence determine the number of calculators the school bought.
(c) Calculate the offered to the school as a percentage.
If the price is p, and the discounted price is q
p = 16200/x
q = p-60 = 16200/x - 60
px = 16200
(p-60)(x+3) = 16200
(16200/x - 60)(x+3) = 16200
x = 27
so, p=600
check:
27 @ 600 = 16200
30 @ 540 = 16200
60 discount is 10%
Analyse futher
(a)
(i) The original price of each calculator can be expressed as:
Original price = Total cost / Number of calculators
Let's denote the original price as P.
So, P = 16200 / x
(ii) The price of each calculator after the discount can be expressed as:
Discounted price = Original price - Discount per calculator
Let's denote the discounted price as D.
So, D = P - 60
(b)
The school was able to get three extra calculators for the same amount of money, which means the new total cost is still Ksh 16200.
The new total cost can be expressed as:
New total cost = (x + 3) * D
Setting this equal to the original total cost, we have:
(x + 3) * D = 16200
(c)
To calculate the discount as a percentage, we can use the formula:
Discount percentage = (Discount per calculator / Original price) * 100
Substituting the values, we get:
Discount percentage = (60 / P) * 100
(a)
(i) The original price of each calculator can be calculated by dividing the total cost by the number of calculators. The expression in terms of x would be:
Original price of each calculator = Total cost / Number of calculators
Original price of each calculator = Ksh 16200 / x
(ii) The price of each calculator after the discount can be calculated by subtracting the discount amount from the original price. The expression in terms of x would be:
Price of each calculator after the discount = Original price of each calculator - Discount per calculator
Price of each calculator after the discount = Ksh 16200 / x - Ksh 60
(b) To form an equation in x and determine the number of calculators the school bought, we consider the fact that the school was able to get three extra calculators for the same amount of money. This means that the cost of the extra calculators should be equal to the discount amount for the original x calculators.
The equation can be set up as follows:
Total cost of the extra calculators = Discount per calculator * x
Total cost of the extra calculators = Ksh 60 * x
Since the total cost for the extra calculators is the same as the original total cost, we can equate the two equations:
Ksh 60 * x = Ksh 16200
Simplifying the equation:
60x = 16200
Dividing both sides by 60:
x = 270
Therefore, the school bought 270 calculators.
(c) To calculate the percentage discount offered to the school, we can use the formula:
Percentage Discount = (Discount per calculator / Original price of each calculator) * 100
Plugging in the values:
Percentage Discount = (60 / (16200 / x)) * 100
Percentage Discount = (60 / (16200 / 270)) * 100
Percentage Discount = 0.1111 * 100
Percentage Discount = 11.11%
The discount offered to the school is 11.11%.