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?

Question

Container A: y =16x+104
Container B:
y=- 2x3+40x+160
(1 point)
• 360 ounces
• 328 ounces
• 232 ounces
• 136 ounces

Answer 1

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