Final answer:
To find the cost of fringe for a regular pentagon mat, calculate the side length by solving x from the given expressions, find the perimeter in inches, convert it to yards, and then multiply by the cost per yard. The total cost for the fringe is $1.88.
Step-by-step explanation:
The question asks us to determine the cost of fringe needed for a mat shaped like a regular pentagon with sides of lengths (x + 5) inches and (4x - 7) inches.
Since the mat is a regular pentagon, all sides are equal, hence we can set (x + 5) equal to (4x - 7) to find the length of a side. Solving this equation, we get x = 4 inches, which means that each side is 9 inches long (since 4 + 5 = 9).
To find the perimeter, we will multiply this length by 5: 9 inches * 5 sides = 45 inches.
Next, we convert the perimeter from inches to yards since fringe is sold by the yard, remembering that there are 36 inches in a yard: 45 inches / 36 inches per yard = 1.25 yards.
The fringe costs $1.50 per yard, so the total cost of the fringe is: 1.25 yards * $1.50 per yard = $1.88.