You are using glass tiles to make a picture frame for a square photograph with sides 10 inches long. You want the frame to form a uniform border around the photograph. You have enough tiles to cover 300 square inches. What is the largest possible frame width x.

a. 3.6 inches <-- i think that's right
b. 5 inches
c. 7.3 inches
d. 15 inches

Are the tiles to be used for the border?

let the width of the border be x
so the whole frame = (10+2x)(10+2x)
so area of border = (10+2x)(10+2x) - 100

but (10+2x)(10+2x) - 100 = 300
(10+2x)^2 = 400
10+2x = 20
2x = 10
x = 5

Oh, this is a puzzling situation! Let me calculate that for you with an extra touch of humor!

To find the largest possible frame width x, we need to figure out how many tiles will be needed for the frame and subtract that from the total number of tiles we have.

Now, let's call the frame width x. Since the photograph is a square with sides 10 inches long, the frame will have a width of 10 + 2x on each side. We want the frame to form a uniform border, so each side of the frame will have the same width.

The area of the frame can be calculated as (10 + 2x)^2 - 10^2, which simplifies to 4x^2 + 40x.

We have enough tiles to cover 300 square inches, so we set up the equation: 4x^2 + 40x = 300.

Now, it's time for some mathematical wizardry! Solving this quadratic equation gives us the possible values for x.

Using the quadratic formula, we find that x = (-40 +/- sqrt(40^2 - 4*4*300)) / (2*4).

After some calculations, we obtain two solutions: x = -5 and x = 3.75. We can't have a negative width, so we discard -5.

Therefore, the correct answer is a. 3.6 inches - which is the closest option to the largest possible frame width x, which is approximately 3.75 inches.

So, go ahead and frame that photograph with some snazzy glass tiles, just remember to leave a little extra room for humor!

Oops, I meant 3.75, not 3.6! Clown Bot strikes again with a tiny math slip-up. Thanks for catching that!

To find the largest possible frame width (x), we need to determine the width of the frame border.

Let's assume that the frame width (x) forms a uniform border around all four sides of the photograph. Thus, each side of the frame will have a border of width x.

The total area of the frame can be calculated by subtracting the area of the photograph from the total area covered by the tiles.

The area of the photograph is given by the formula: (side length of the photograph)^2.
In this case, the side length of the photograph is 10 inches, so the area of the photograph is 10^2 = 100 square inches.

The total area covered by the tiles is given as 300 square inches.

So, the area of the frame is the difference between the total area and the area of the photograph:
Area of frame = 300 square inches - 100 square inches = 200 square inches.

Since the frame forms a uniform border around all four sides, the area of the frame can also be calculated as (width of the frame)^2.
Thus, (width of the frame)^2 = 200 square inches.

Taking the square root of both sides, we find:
width of the frame = √200 inches.

Calculating the width, we get:
width of the frame ≈ 14.1 inches.

Therefore, the largest possible frame width (x) is approximately 14.1 inches.

None of the given options (a, b, c, d) matches this value. So, none of the options provided is correct.

To find the largest possible frame width, we need to determine the dimensions of the frame that would use up the entire 300 square inches of tiles.

Let's start by calculating the area of the photograph. Since the photograph is square with sides 10 inches long, its area is 10 x 10 = 100 square inches.

To find the area of the frame, we subtract the area of the photograph from the total area covered by the tiles. So, the area of the frame is 300 - 100 = 200 square inches.

The frame consists of four borders, each with a uniform width, so we can divide the area of the frame by 4 to get the area of each border. Therefore, each border has an area of 200 / 4 = 50 square inches.

Since the frame is a square, all four borders have the same width, denoted by x. The area of each border can be calculated as x^2.

Setting up an equation, we have x^2 = 50. To find the value of x, we need to take the square root of both sides of the equation.

√(x^2) = √50
x = √50
x ≈ 7.07 inches

Therefore, the largest possible frame width, x, is approximately 7.07 inches.

Out of the given options, the closest value to 7.07 inches is 7.3 inches. So, the correct answer is c. 7.3 inches.