A teacher wants to buy a box of x pencils worth RM12.00 as a present for the winner of a quiz. If each pencil is given a discount of RM00.10, the teacher will get to buy 4 more pencils with the same amount of money.
i)Calculate the number of pencils that the teacher can buy after the discount. ii)Calculate the original price of each pencil.
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The teacher wants to buy x pencils worth RM12.00. If each pencil is given a discount of RM00.10, the teacher will get to buy 4 more pencils with the same amount of money. Calculations of the prices and quantities are shown below:
Before discount
Let the price of 1 pencil be p1
Total pencils in a box = q1
Total price per box = p1q1 = 12
p1 = 12/q1 equation 1
After discount
Discount on one pencil = 0.10
Let the price of 1 pencil after discount be p2 = p1-0.10
Let the quantity of pencils after discount be q2 = q1+4
New price is discounted price and new quantity is 4 more than old quantity
Discounted price × (old qty + 4) = 12
(p1-0.10) × (q1 + 4) = 12 equation 2
p1q1+ 4p1 – 0.10q1 – 0.4 = 12
12 – 0.10q1 + 4p1 – 0.4 = 12
4p1 - 0.10q1 = 0.4
0.10q1 = 4p1 - 0.4
q1 = 40p1 - 4
since p1 = 12/q1
q1 = 480/q1 - 4
q1 + 4 = 480/q1
q1 × (q1 + 4) = 480
splitting 480 into the same form of equation
q1× (q1 + 4) = 20 × (20 + 4) = 480
so q1 = 20
Number of pencils that the teacher can buy after discount (q2) = 20 + 4 = 24
Original price of each pencil (p1) = 12/20 = 0.6
p2 = 0.6 – 0.10 = 0.50