To find the point when the two containers hold the same amount of water, we need to set the two equations equal to each other and solve for x:
16x + 104 = -2x^2 + 40x + 160
Rearranging terms:
2x^2 + 24x + 56 = 0
Dividing by 2:
x^2 + 12x + 28 = 0
Factoring:
(x + 4)(x + 7) = 0
Setting each factor to zero:
x = -4 or x = -7
Since time cannot be negative, the containers will hold the same amount of water after 7 minutes.
Plugging in x = 7 to either equation:
Container A: y = 16(7) + 104 = 232 ounces
Container B: y = -2(7)^2 + 40(7) + 160 = 232 ounces
Therefore, the containers will hold 232 ounces of water when they hold the same amount.
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 equals 16 x plus 104
Container B: y equals negative 2 x squared plus 40x plus 160
(1 point)
Responses
360 ounces
360 ounces
328 ounces
328 ounces
232 ounces
232 ounces
136 ounces
136 ounces
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1 answer