Question

An advertising company charges $40 per half-page advertisement and $75 per full-page advertisement. Michael has a budget of $800 to purchase 13 advertisements. Define variables, write a system of equations, and determine how many half-page and full-page advertisements Michael purchases. Show your work."

Answer 1

Michael purchases 5 half-page advertisements and 8 full-page advertisements.

Step-by-step explanation:

Let's define the following variables:

x = number of half-page advertisements

y = number of full-page advertisements

Now, we can create a system of equations:

Equation 1: 40x + 75y = 800 (since the total cost of the advertisements should be $800)

Equation 2: x + y = 13 (since the total number of advertisements should be 13)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiplying Equation 2 by 40, we get:

40x + 40y = 520

Subtracting this equation from Equation 1, we eliminate x:

35y = 280

Dividing both sides by 35, we find y = 8.

Substituting this value back into Equation 2, we can find x:

x + 8 = 13

x = 5.

Therefore, Michael purchases 5 half-page advertisements and 8 full-page advertisements.