A yoga studio charges a $36 membership fee and a $20.60 per month for 10 classes. A Martial Arts studio charges a $20 membership fee and $22.20 per month for 10 classes. Your friend belongs to the yoga studio the same month you belong to the Martial Arts studio. After how many months is your friend's total cost the same as your total cost?

A yoga studio charges a $36 membership fee and a $20.60 per month for 10 classes. A Martial Arts studio charges a $20 membership fee and $22.20 per month for 10 classes. Your friend belongs to the yoga studio the same month you belong to the Martial Arts studio. After how many months is your friend's total cost the same as your total cost?

Question
A yoga studio charges a $36 membership fee and a $20.60 per month for 10 classes. A Martial Arts studio charges a $20 membership fee and $22.20 per month for 10 classes. Your friend belongs to the yoga studio the same month you belong to the Martial Arts studio. After how many months is your friend's total cost the same as your total cost?

Answers (1)

2021-01-03
Let m be the number of months.
The yoga studio charges $20.60 per month so the monthly cost after mm months is 20.60m dollars. The studio also charges a membership fee of $36 so your friend's total cost is 20.60m+36 dollars.
The martial arts studio charges $22.20 per month so the monthly cost after mm months is 22.20m dollars. The studio also charges a membership fee of $20 so your total cost is 22.20m+20 dollars.
If your total cost and your friend's total cost are the same, then:
20.60m+36=22.20m+20
36=1.60m+20
16=1.60m
10=m
Your friend's total cost will then be the same as your total cost after 10 months.
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