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=- 2x3+40x+160
(1 point)
• 360 ounces
• 328 ounces
• 232 ounces
• 136 ounces
To find the amount of water held by each container when they have the same amount, we need to set the two equations equal to each other and solve for x:
16x + 104 = -2x^3 + 40x + 160
0 = -2x^3 + 24x + 56
0 = -x^3 + 12x + 28
By inspection, one of the solutions to this equation is x = 2, as in the equation x - 2 = 0. This means that after 2 minutes, both containers will have the same amount of water.
Now, substitute x = 2 into either equation to find the amount of water they hold at that time:
y = 16(2) + 104 = 32 + 104 = 136 ounces
Therefore, when the containers hold the same amount of water, they both hold 136 ounces. So the answer is:
- 136 ounces