<u>Answer:
</u>
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.
<u>Solution:
</u>
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.
