Rachel and Sarah belong to different gyms. Rachel's gym charges a one-time registration fee of $15 and then charges $35 per month. Whereas Sarah only pays $25 per month but had to pay a $75 registration fee. After how many months will Rachel and Sarah have spent the same amount on their gym memberships?

Question

marigirl · Answer

Develop two equations, then you can either graph it and find its intercepts or make both the equations equal to each other and solve for x
Rachel: y=35x+15  where x stands for the number of months
Sarah: y=25x+75

marigirl · Answer

Then we can make both equations equal to each other to find the point of intersection (where both gyms would cost the same)
$$35x+15=25x+75$$
$$35x-25x=75-15$$
$$10x=60$$
$$x=6$$

Therefore it both the gyms would cost the same if they wish to attend for up to 6 months.

marigirl · Answer

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