a photo is 6 inches wide. it is placed inside a frame with a border that is x inches wide. the total width of the photo and the frame is 9 inches. write an equation to model the situation, then solve the equation to find the width of the border.
Let's assume the width of the border is x inches.
The total width of the photo and the frame can be calculated by adding the width of the photo and twice the width of the border:
6 + 2x
According to the given information, the total width of the photo and the frame is 9 inches. We can set up the following equation:
6 + 2x = 9
Now, we can solve the equation to find the width of the border:
6 + 2x = 9
Subtract 6 from both sides: 2x = 3
Divide both sides by 2: x = 1.5
Therefore, the width of the border is 1.5 inches.
Let's call the width of the border "b".
The total width of the photo and the frame is 9 inches, which means the width of the photo plus the width of the frame is equal to 9 inches: 6 inches (width of the photo) + b inches (width of the border) = 9 inches.
To solve the equation, we need to isolate the variable "b" on one side of the equation. We can do that by subtracting 6 inches from both sides of the equation:
6 inches + b inches - 6 inches = 9 inches - 6 inches.
This simplifies to:
b inches = 3 inches.
Therefore, the width of the border is 3 inches.
To solve this problem, let's use the following steps:
Step 1: Define the variables:
- Let x represent the width of the border.
Step 2: Write the equation:
The total width of the photo and frame is 9 inches. Since the photo is 6 inches wide, we can express the total width as the sum of the photo width and twice the border width (because there are two borders - one on the left and one on the right):
6 + 2x = 9
Step 3: Solve the equation:
Subtract 6 from both sides of the equation:
2x = 9 - 6
2x = 3
Divide both sides of the equation by 2:
x = 3/2
x = 1.5
Therefore, the width of the border is 1.5 inches.