Question

A newspaper charges $50 per half-page ad and $80 per full-page ad. Gavin has a budget of $750 to purchase 12 advertisements.

a. Define a variable for each unknown. Write a system of equations to represent the situation.
b. How many half-page advertisements does Gavin purchase?
c. How many full-page advertisements does Gavin purchase?

Answer 1

By setting up a system of equations based on the cost of the ads and the total budget, we solve for x and y, which represent half-page and full-page advertisements respectively. Gavin buys 7 half-page advertisements and 5 full-page advertisements.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's define x as the number of half-page advertisements and y as the number of full-page advertisements that Gavin wants to purchase. Since each half-page ad costs $50 and each full-page ad costs $80, and Gavin has a budget of $750 for 12 ads, we can write the following equations:

• 50x + 80y = 750 (Budget constraint)
• x + y = 12 (Number of advertisements)

To find the number of half-page and full-page ads, we can solve this system of equations simultaneously. Multiply the second equation by 50 to help with elimination:

• 50x + 80y = 750
• 50x + 50y = 600

Subtract the second equation from the first:

• 30y = 150

Dividing both sides by 30 gives us:

• y = 5

We substitute y = 5 into x + y = 12 to find the value of x:

• x + 5 = 12
• x = 7

Gavin purchases 7 half-page advertisements and 5 full-page advertisements.