Jamie has a garden that is 20 meters by 30 meters. He wants to have a concrete pathway that is the same width all around the edge of the garden. If Jamie has enough concrete to cover 336 square meters, how wide will the pathway be?
First, we need to calculate the total area of the garden:
Total area of the garden = 20 meters * 30 meters = 600 square meters
Let's assume the width of the pathway is x meters. The inner area of the garden (excluding the pathway) can be calculated as:
Inner area of the garden = (20 - 2x) * (30 - 2x)
Now, we can write the equation for the total area of the garden plus the area of the pathway:
Total area = Inner area of the garden + area of the pathway
600 + 336 = (20 - 2x) * (30 - 2x)
936 = 600 - 40x - 60x + 4x^2
936 = 600 - 100x + 4x^2
Rearranging the equation:
4x^2 - 100x + 336 = 0
Dividing the equation by 4:
x^2 - 25x + 84 = 0
Now, we can factorize the equation:
(x - 21)(x - 4) = 0
So, x = 21 or x = 4
Since the width of the pathway cannot be greater than half the width or length of the garden, the width of the pathway will be 4 meters.