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.
(a)
(i) The original price of each calculator can be expressed as:
Original price = Total cost / Number of calculators
Original price = Ksh 16200 / x
(ii) The price of each calculator after the discount can be expressed as:
Price after discount = Original price - Discount
Price after discount = (Ksh 16200 / x) - Ksh 60
(b) To form an equation in x, we consider that the school was able to get three extra calculators for the same amount of money. This implies that the cost of the extra calculators is equal to the discount offered.
Cost of extra calculators = Discount
Price after discount * 3 = Ksh 60
[(Ksh 16200 / x) - Ksh 60] * 3 = Ksh 60
(c) To calculate the discount percentage, we can use the following formula:
Discount percentage = (Discount / Original price) * 100
Discount percentage = (Ksh 60 / ((Ksh 16200 / x) - Ksh 60)) * 100
(a) Let's solve the problem step by step:
(i) Original price of each calculator:
If the school planned to buy x calculators for a total cost of Ksh 16200, then the original price of each calculator can be calculated by dividing the total cost by the number of calculators:
Original price per calculator = Total cost / Number of calculators
Original price per calculator = 16200 / x
So the expression in terms of x for the original price of each calculator is 16200 / x.
(ii) Price of each calculator after the discount:
The supplier offers a discount of Ksh 60 per calculator. So, the price of each calculator after the discount can be calculated by subtracting the discount from the original price per calculator:
Price after discount per calculator = Original price per calculator - Discount
Price after discount per calculator = 16200 / x - 60
Therefore, the expression in terms of x for the price of each calculator after the discount is 16200 / x - 60.
(b) To form an equation in x and determine the number of calculators the school bought, we can use the information given that the school was able to get three extra calculators for the same amount of money.
The original plan was to buy x calculators at the original price per calculator. So, the total cost for x calculators would be:
Total cost = Original price per calculator * Number of calculators
Total cost = (16200 / x) * x
Total cost = 16200
But the school was able to get three extra calculators for the same total cost, which means they paid the same amount of money for (x + 3) calculators. So we can set up an equation:
(16200 / x) * (x + 3) = 16200
Simplifying the equation:
16200(x + 3) = 16200 * x
16200x + 48600 = 16200x
48600 = 16200x - 16200x
48600 = 0
Since 48600 = 0 has no solution, it means that there is no value of x that satisfies the equation. Therefore, the given information might be inconsistent or inaccurate.
(c) Since we were not able to determine the number of calculators bought in part (b), we cannot calculate the percentage discount offered to the school.