17
Select the correct answer.
It takes Greg and Nikki a total of 40 minutes to paint a room if they work together. If Greg works alone, he takes 18 minutes longer to paint he
room than Nikki takes if she works alone.
When x represents the number of minutes it takes Nikki to paint the room working alone, the situation is represented by this equation:
+
= 40
Which value is a solution of the rational equation that must be discarded because of the context?
OA. x = 0
OB. x= -10
OC. X = -18
OD. x= -72
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MrRoyal MrRoyal · Answer 1 · 2021-12-22T17:26:13+01:00

The value that is a solution of the rational equation that must be discarded because of the context is (b) x = -10

The equation is given as:

[tex]\frac 1x + \frac{1}{x + 18} = \frac{1}{40}[/tex]

Take the LCM

[tex]\frac{x + 18 + x}{x(x + 18)} = \frac{1}{40}[/tex]

This gives

[tex]\frac{2x + 18}{x(x + 18)} = \frac{1}{40}[/tex]

Cross multiply

[tex]40(2x + 18) =x(x + 18)[/tex]

Expand

[tex]80x + 720 =x^2 + 18x[/tex]

Collect like terms

[tex]x^2 + 18x - 80x -720 = 0[/tex]

[tex]x^2 - 62x -720 = 0[/tex]

Using a graphing calculator, we have:

[tex]x = 72\ or\ x =-10[/tex]

The value of x cannot be negative, because of the context.

So, the value that is a solution of the rational equation that must be discarded because of the context is (b) x = -10

Read more about rational equations at:

https://brainly.com/question/18446103