I need help with this because this extremely confuses me.​

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  6 months

Step-by-step explanation:

There are a couple of ways you can work a problem like this. I like to start by looking at the differences in fixed costs and in monthly fees.

The gym with a higher fixed cost has a lower monthly fee, and vice versa. This is usually the case for algebra problems.

The difference in "fee to join" is $200 -20 = $180.

The difference in "charge per month" is $40 -10 = $30.

So, if I pay $180 more up front, I can save $30 per month. It will take me ...

  $180/$30 = 6

months for the total of my savings to match the cost I paid up-front.

Another way to work problems like this is to write an equation for the cost of membership at each gym. If we let x represent months of membership, the cost (g) at Grim's gym is ...

  g = up-front cost + (monthly cost) times x

  g = 200 +10x

Similarly the cost (m) at Mandy's gym is ...

  m = 20 +40x

The question asks the value of x (number of months) it will take for the costs to be equal.

  g = m

  (200 +10x) = (20 +40x)

  180 +10x = 40x . . . . . . . . . subtract 20 from both sides

  180 = 30x . . . . . . . . . . . . . . subtract 10x from both sides

You may recognize this equation as saying the difference in join fees is equal to the difference in monthly charges after x months. That is where we started at the beginning.

  180/30 = 30x/30 . . . . . . divide both sides of the equation by 30

  6 = x . . . . . simplfy

It will take 6 months for the total cost to be equal for Grim and Mandy.

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step-by-step explanation: vsfdvsfvd