Question

(90 Points)

(Score for Question 1: ___ of 10 points)
A local newspaper charges $42 per half-page advertisement and $86 per full-page advertisement. Kathryn has a budget of $1192 to purchase 20 advertisements.
• Define a variable for each unknown.
• Write a system of equations to represent the situation.
• How many full-page advertisements does Kathryn purchase?
• Show your work.
• How many half-page advertisements does Kathryn purchase?
Show your work.

Answer 1

Let x = number of half-page advertisements

Let y = number of full-page advertisements

`\begin{cases} 42x + 86y = 1192\\ x + y = 20\end{cases}`

8 full-page advertisements

12 half-page advertisements

Explanation:

Definition of variables

Let x = number of half-page advertisements

Let y = number of full-page advertisements

Given information:

• cost per half-page advertisement = $42
• cost per full-page advertisement = $86
• total budget = $1192
• number of advertisements to purchase = 20

Using the given information, we can write a system of equations:

Equation 1: 42x + 86y = 1192

Equation 2: x + y = 20

To solve the system of equations, rearrange Equation 2 to make x the subject:

⇒ x = 20 - y

then substitute this into Equation 1 and solve for y:

⇒ 42(20 - y) + 86y = 1192

⇒ 840 - 42y + 86y = 1192

⇒ 840 + 44y = 1192

⇒ 44y = 352

⇒ y = 8

Substitute the found value of y into Equation 2 and solve for x:

⇒ x + 8 = 20

⇒ x = 12

Therefore, Kathryn purchased:

• 8 full-page advertisements
• 12 half-page advertisements