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The equation 9+12m=6+15(m-1) models the following situation: Movie-rental company A charges a sign-up fee of $9 plus $12 per month, and company B charges $6 for the first month plus $15 per month after that. At a certain number of months, the cost of the two companies is equal

Respuesta :

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Start by distributing the 15 to the (m-1). 9+12m=6+15m-15. Then combine like terms. 9+12m=15m-9. Next move the variable all to one side, it doesn't matter which variable you choose. I'll use 12m so when I subtract I am still left with a postive coefficient. To move the 12m we subtract it from both sides of the equation. We are left with 9=3m-9. Next we isolate the m by canceling out the 9. We do this by adding 9 to both sides. We are left with 18=3m. Finally, to completely isolate the m, we must divide both sides by the coefficient, 3. The result is 6=m. The answer is 6 months. You can check this by plugging 6 back into the equation where there is an m. (sorry for the long answer)

To solve the problem we will solve the expression given to us.

Expression

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

At 6 months the cost of the two companies is equal.

Given to us

  • equation, 9+12m=6+15(m-1)
  • Movie-rental company A charges a sign-up fee of $9 plus $12 per month.
  • Movie-rental company B charges $6 for the first month plus $15 per month after that

Cost of both months will be equal

It is already given to us the equation at which the cost of both the company will be the same, solving the equation we get.

[tex]9+12m=6+15(m-1) \\\\9+12m = 6+15m -15\\\\9-6+15 = 15m-12m\\\\18 = 3m\\\\m=\dfrac{18}{3}\\\\m= 6[/tex]

Hence, at 6 months the cost of the two companies is equal.

Learn more about Expression:

https://brainly.com/question/13947055

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