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One moving company charges $800 plus $16 per hour.another moving company charges $720 plus $21 per hour. At what number of hours will the charge by both companies be the same?

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ProfessorAlvarez

Hello there!

We are trying to find when both companies will charge the same rate for moving stuff.

This means that we have to find the "point of intersection" between them.

Lets make equations to make this easier.

Company one:

  • Charges $800
  • $16 per hour

This makes y = 16x + 800

Company two:

  • Charges $720
  • $21 per hour

This makes y = 21x + 720

What we would do is put the equation together and solve.

Solve:

16x + 800 = 21x + 720

-21x              -21x

-5x + 800 = 720

      - 800    -800

-5x = -80

x = 16

In 16 hours, both companies prices will be the same.

I hope this helps!

Best regards,

MasterInvestor

Answer:

16 hours.

Step-by-step explanation:

Let x represent number of hours.

We have been given that a moving company charges $800 plus $16 per hour. The total cost of the company moving for x hours would be [tex]16x+800[/tex].

Another moving company charges $720 plus $21 per hour. The total cost of the company moving for x hours would be [tex]21x+720[/tex].

Now, we will equate both expression to solve for x.

[tex]21x+720=16x+800[/tex]

[tex]21x-16x+720=16x-16x+800[/tex]

[tex]5x+720=800[/tex]

[tex]5x+720-720=800-720[/tex]

[tex]5x=80[/tex]

[tex]\frac{5x}{5}=\frac{80}{5}[/tex]

[tex]x=16[/tex]

Therefore, at 16 hours the amount charged by both companies will be same.

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