A pool measuring 16 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 832 square meters, what is the width of the path?

Let X be the width of the path.

The width of the path would be the width of the pool plus 2x, so 2x + 16

The length of the path would be the length of the pool plus 2x, so 2x+22

The total area is 832 square feet.

Area is found by multiplying the length by the width.

So you have:

(2x+16) (2x+22) = 832

Use the Foil Method:

(2x+16) (2x+22) = 4x^2 + 76x+352

Now you have:

4x^2 + 76x+352 = 832

Subtract 832 from both sides:

4x^2 + 76x+352-832 = 0

Simplify:

4x^2 + 76x - 480

Factor the left side:

4 (x-5) (x+24) = 0

Divide both sides by 4:

(x-5) (x+24) = 0

Set both parenthesis to equal 0 and solve for x:

x=5 and x = - 24

The width of the path cannot be a negative number, so the width is 5 meters.