Final answer:
To find the width of the border, subtract the area of the picture from the total area of the picture and the border. The width of the border is approximately 0.527 inches.
Step-by-step explanation:
To find the width of the border, we need to subtract the area of the picture from the total area of the picture and the border. The area of the picture is 7 inches by 5 inches, which is 35 square inches.
The area of the picture and the border is given as 80 square inches.
So, the area of the border is 80 - 35 = 45 square inches.
Since the border has a uniform width, we can assume that the width of the border is the same on all sides.
Let's say the width of the border is x inches. Since the overall dimensions of the border and the picture combined are 7 + 2x inches by 5 + 2x inches, the area of the border can be calculated as
(7 + 2x)(5 + 2x) - 35 = 45.
Simplifying this equation, we get
4x^2 + 24x - 10 = 0.
Solving this quadratic equation, we find that x ≈ 0.527 inches.
Therefore, the width of the border is approximately 0.527 inches.