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 containors hold the same amount of water, how much water do they hold?
container a : y=16x+104
containor b : y=-2x^2+40x+160
360 ounces
328 ounces
232 ounces
136 ounces
To find the time after the start when the containers hold the same amount of water, we need to set the equations equal to each other and solve for x.
16x + 104 = -2x^2 + 40x + 160
Combine like terms:
0 = -2x^2 + 24x + 56
Divide through by -2:
0 = x^2 - 12x - 28
This quadratic equation can be factored:
0 = (x - 14)(x + 2)
Setting each factor equal to zero and solving for x:
x - 14 = 0 --> x = 14
x + 2 = 0 --> x = -2
Since time cannot be negative, we discard x = -2 and conclude that x = 14.
To find the amount of water the containers hold at this time, substitute x = 14 into either equation and solve for y:
For container a:
y = 16(14) + 104 = 360 ounces
Therefore, when the containers hold the same amount of water, they hold 360 ounces.