Water is added to two containers for 16 minutes. The equations below model the ounces of water, y, in each container after x minutes. At the time after the start when the containers hold the same amount of water, how much water do they hold?
Container A: y=16x+104
Container b: y=-2x^2+40x+160
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To find the time when the containers hold the same amount of water, we need to set the two equations equal to each other:
16x + 104 = -2x^2 + 40x + 160
Rearranging this equation, we get:
2x^2 + 24x - 56 = 0
Dividing by 2, we get:
x^2 + 12x - 28 = 0
Factoring this quadratic equation, we get:
(x + 14)(x - 2) = 0
So, x = -14 or x = 2. Since time cannot be negative, x = 2.
Substitute x = 2 back into either equation to find the amount of water each container holds after 2 minutes:
Container A: y = 16(2) + 104 = 32 + 104 = 136 ounces
Container B: y = -2(2)^2 + 40(2) + 160 = -8 + 80 + 160 = 232 ounces
Therefore, after 2 minutes, both containers hold 136 ounces of water.