MATH SOLVE

2 months ago

Q:
# 9. Water is added to two containers for 20 minutes. The equations below model the ounces ofwater, y, in each container after x minutes. At the time when the containers hold the sameamount of water, how much water do they hold?Container A: y = 62x+48Container B: y=-2x^2+80x+120234 ounces482 ounces792 ounces920 ounces

Accepted Solution

A:

Answer:792 ouncesStep-by-step explanation:The equations below model the ounces of water, y, in each container after x minutes.
Container A: y = 62x + 48
Container B: y = -2x² + 80x + 120
Now, at a time when both the containers hold the same amount of water, is given by
62x + 48 = -2x² + 80x + 120
⇒ 2x² - 18x - 72 = 0
⇒ x² - 9x - 36 = 0
⇒ x² - 12x + 3x - 36 = 0
⇒ (x - 12)(x + 3) = 0
Hence, x = 12 or - 3.
But x can not be negative.
So, x = 12 minutes.
Therefore, after 12 minutes both the container will have the same amount of water and the quantity is = 62 × 12 + 48 = 792 ounces. (Answer)