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.

.50p+3 = .80p-1.50

.3p = 4.50
p = 15

so, 15 pencils cost $7.50, meaning he started out with $10.50
15 notepads cost $12.00, so he'd be $1.50 short.

Let's assume that "x" is the number of pencils Casper purchased.

According to the given information, Casper bought the pencils at $0.50 each. Therefore, the total cost of the pencils can be calculated as:
Cost of pencils = x * $0.50 = $0.50x

After purchasing the pencils, Casper had $3 left. This means that the total amount he had before buying the pencils was $3 + Cost of pencils. Therefore, we can write the equation as:
$3 + $0.50x = Total amount before purchasing pencils

Similarly, Casper wanted to buy the same number of note pads at $0.80 each. Therefore, the total cost of the note pads would be:
Cost of note pads = x * $0.80 = $0.80x

However, he would be short $1.50 to buy the note pads. So, the total amount he had before buying the note pads would be $1.50 more than Cost of note pads. Thus, we can write the equation as:
$1.50 + Cost of note pads = Total amount before purchasing note pads

Now, to solve the problem, we need to set up the equation by replacing the values:
$3 + $0.50x = $1.50 + $0.80x

To simplify the equation, we can move all the x terms to one side:
$3 - $1.50 = $0.80x - $0.50x
$1.50 = $0.30x

Finally, to find the value of x, we need to solve for it by isolating x:
$1.50 / $0.30 = x
5 = x

Therefore, Casper purchased 5 pencils.

To write a linear equation, let's first define some variables:

Let "x" be the number of pencils Casper purchased.

Since each pencil costs $0.50, the total cost of the pencils can be calculated as 0.50x.

After purchasing the pencils, Casper had $3 left. This can be represented as $3 = 0.50x.

However, this equation only represents one aspect of the problem. We also know that Casper would be short $1.50 if he wanted to buy the same number of notepads at $0.80 each. This means the total cost of the notepads is 0.80 multiplied by the same number "x" of pencils, which gives us 0.80x.

To represent Casper being short $1.50, we can write the equation 0.80x - $1.50.

Combining both equations, we get:
0.50x = $3 and 0.80x - $1.50

Simplifying the second equation, we can rewrite it as 0.80x = $1.50.

Now, we have two equations:
0.50x = $3
0.80x = $1.50

To solve for "x," we can divide both sides of the first equation by 0.50:
x = $3 / 0.50
x = 6

So, Casper purchased 6 pencils.