Casper bought some pencils at .50 each. He had $3 left after the purchase. If he wanted to buy the same number of note pads at .80 each, he would be short 1.50. Write a linear equation for the number of pencils he purchased. Then solve it.

Answer:   Required linear equation to get number of pencils purchased by Casper is 3x – 45 = 0 where x represents number of pencils and number of pencils Casper purchased = 15. Solution: Let’s assume number of pencils purchased by Casper = x As given price of each pencil is 0.50 , so price of x pencils = 0.50x = 0.5x Also given that she was left with $3 after buying x pencils. So initial amount which was with casper = price of x pencils + amount he was left with. => Initial amount with Casper = 0.5x + 3    ------(1) Now consider second scenario  If Casper wanted to buy same number of notepad at price of 0.80 each , then Total amount need for x notepad = 0.80x = 0.8x But its also given that he will be short of $1.5. So initial amount with Casper = 0.80x – 1.5 ------(2) On equating initial amount with casper using equation (1) and equation(2) we get 0.5x + 3 = 0.8x – 1.5 => 0.8x – 0.5x = 3 + 1.5 => 0.3x = 4.5 => 0.3x – 4.5 = 0  => 3x – 45 = 0 So linear equation for x that is number of pencils he purchased is 3x – 45 = 0 where variable x represents number of pencils. On solving the linear equation 3x – 45 = 0 for x we get 3x = 45 x = 15 Hence required linear equation to get number of pencils purchased by Casper is 3x – 45 = 0 where x represents number of pencils and number of pencils Casper purchased = 15.