A photo is 4 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 7 inches. Write an equation to model the situation. Then solve the equation to find the width of the border.
Let's represent the width of the border as "b."
The total width of the photo and the frame is the sum of the width of the photo and the width of the border: 4 inches + b inches.
According to the problem, the total width of the photo and the frame is 7 inches.
Therefore, we can write the equation:
4 + b = 7
Now, let's solve the equation to find the width of the border (b):
Subtract 4 from both sides of the equation:
b = 7 - 4
b = 3
Therefore, the width of the border is 3 inches.
Let's call the width of the border "x".
The width of the photo is given as 4 inches.
The total width of the photo and the frame is 7 inches.
So, we can write the equation:
Width of the photo + Width of the border + Width of the border = Total width of the photo and frame
Plugging in the given values and variables, we have:
4 + x + x = 7
Simplifying the equation, we get:
4 + 2x = 7
Now, let's solve the equation to find the width of the border:
Subtracting 4 from both sides, we have:
2x = 3
Dividing both sides by 2, we get:
x = 3/2
Therefore, the width of the border is 3/2 inches.
To solve this problem, let's first define the variables involved:
Let "x" represent the width of the border.
Let "y" represent the width of the photo (given as 4 inches).
Let "z" represent the total width of the photo and frame (given as 7 inches).
We can model the situation with the following equation:
y + x + x = z
Since the photo is placed inside the frame, we have two identical border widths on both sides of the photo, which is why we add "x" twice.
Now, let's substitute the given values into the equation:
4 + x + x = 7
Combine like terms:
2x + 4 = 7
Next, isolate the variable by subtracting 4 from both sides of the equation:
2x = 7 - 4
2x = 3
Finally, divide both sides by 2 to solve for "x":
x = 3/2
x = 1.5
Therefore, the width of the border is 1.5 inches.