Question

9. Water is added to two containers for 16 minutes. The equations below model the ounces of

Answer 1

The two containers hold 328 ounces at the they hold same amount of water.

Step-by-step explanation:

The equations below model the ounces of  water, y, in each container after x minutes.

$y = 16x + 104$

$y = -2x^{2} +40x+160$

At the time after the start when the containers hold  the same amount of water, the two equations must be equal.

⇒ $16 x + 104 = -2x^{2} + 40 x + 160$

The first step is to divide everything by 2 to make it simplified.

⇒ $8 x + 52 = - x^2 +20 x + 80$

Now put everything on the left .

$x^2 + 8 x - 20 x + 52 - 80 = 0$

Add the like terms together to further reduce the equation

$x^2 - 12 x - 28 = 0$

Factorizing the equation to find the roots of the equation.

Here, b = -12 and c = -28

where,

• b is the sum of the roots ⇒ -14 + 2 = -12
• c is the product of the roots ⇒ -14 × 2 = -28

• Therefore, (x-14) (x+2) = 0
• The solution is x = -2 or x = 14

Take x = 14  and substitute in any of the given two equations,

⇒ $y = 16(14) + 104$

⇒ $y =224+104$

⇒ 328 ounces

∴ The two containers hold 328 ounces at the they hold same amount of water.