Question

comic books cost $2 each and magazines cost $4 each. if you want to spend exactly $30 and you buy 3 magazines, how many comic books can you buy? you just found that when m = 3, c must equal 9 to make the equation true. what does that mean?
2c + 4m = 30
2c + 4·3 = 30
2c + 12 = 30
c = 9
if you buy 3 magazines, then you can buy
comic books and spend exactly
dollars.

Explanation:

Step1: Define variables given

Let \(c\) = number of comic books, \(m = 3\) (magazines bought)

Step2: Substitute \(m=3\) into equation

\(2c + 4(3) = 30\)

Step3: Simplify the constant term

\(2c + 12 = 30\)

Step4: Isolate the variable term

\(2c = 30 - 12 = 18\)

Step5: Solve for \(c\)

\(c = \frac{18}{2} = 9\)

The value \(c=9\) when \(m=3\) means purchasing 3 magazines and 9 comic books uses exactly the $30 budget, satisfying the cost equation.

Answer:

If you buy 3 magazines, then you can buy 9 comic books and spend exactly 30 dollars.

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