Question

If 3 computer disks and 5 notebooks cost $7.50 and 4 computer disks and 2 notebooks costs $6.50, how much does 1 computer disk cost?

Answer 1

Let the cost of one computer disk be \( x \) dollars and the cost of one notebook be \( y \) dollars. We can formulate the following equations based on the information given:

1. For 3 computer disks and 5 notebooks:
\[
3x + 5y = 7.50
\]
2. For 4 computer disks and 2 notebooks:
\[
4x + 2y = 6.50
\]

Now, we can solve this system of equations. We will start with the second equation and simplify it:

\[
4x + 2y = 6.50
\]
Dividing the entire equation by 2 gives us:
\[
2x + y = 3.25 \quad \text{(Equation 2)}
\]

Next, we will solve for \( y \) in terms of \( x \) from Equation 2:
\[
y = 3.25 - 2x
\]

Now substituting this expression for \( y \) into Equation 1:
\[
3x + 5(3.25 - 2x) = 7.50
\]

Expanding this:
\[
3x + 16.25 - 10x = 7.50
\]

Combining like terms gives:
\[
-7x + 16.25 = 7.50
\]

Now, isolating \( x \):
\[
-7x = 7.50 - 16.25
\]
\[
-7x = -8.75
\]
\[
x = \frac{-8.75}{-7} = 1.25
\]

Thus, the cost of one computer disk is:
\[
\boxed{1.25}
\]

To verify, we can substitute \( x = 1.25 \) back to find \( y \):
Using \( y = 3.25 - 2x \):
\[
y = 3.25 - 2(1.25) = 3.25 - 2.50 = 0.75
\]

Now we verify the original equations:
1. For the first equation:
\[
3(1.25) + 5(0.75) = 3.75 + 3.75 = 7.50 \quad \text{(holds true)}
\]
2. For the second equation:
\[
4(1.25) + 2(0.75) = 5.00 + 1.50 = 6.50 \quad \text{(holds true)}
\]

Both equations are satisfied, confirming our solution. The cost of one computer disk is indeed:
\[
\boxed{1.25}
\]