Question

The amount of water in a bathtub as it drains can be modeled by this equation with y representing the number of gallons of water in the tub and x representing the time, in minutes, that the tub has been draining.

y=−7.3x+39.7

After how many minutes will the tub have 17.8 gallons of water remaining?

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min

Answer 1

After 3 minutes the tub will have 17.8 gallons of water remaining.

Explanation:

Given : The amount of water in a bathtub as it drains can be modeled by the equation,

y = −7.3 x + 39.7 .............(1)

Where, y representing the number of gallons of water in the tub and x representing the time, in minutes.

We have to determine the time when the tub have 17.8 gallons of water remaining.

That is y = 17.8

Substitute y = 17.8 in (1) , we get,

⇒ y = −7.3 x + 39.7

⇒ 17.8 = −7.3 x + 39.7

Solve for x , we get,

⇒ 17.8 - 39.7 = −7.3 x

⇒ - 21.9 = −7.3 x

⇒ 21.9 = 7.3 x

⇒ x = 3

Thus, after 3 minutes the tub will have 17.8 gallons of water remaining.

Answer 2

Given function:
y=-7.3x+39.7
Where y= number of gallons of water
and x= number of minutes
Put value of y=17.8 gallons and solving for x.
17.8=-7.3x+39.7
Subtract 39.7 from both sides
-21.9=-7.3x
Divide both sides by -7.3
3=x
or
x=3 minutes
After 3 minutes the water in the tub will be 17.8 gallons.

Answer: 3 minutes