Question 1019199: Write a system of equations that corresponds to the situation.
- Lisa spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym and spends the rest of the year with the second gym. The membership to the first gym costs $75 per month, while the membership for the second gym costs $50 per month. She ends up spending a total of $775 over the course of the year.
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! So we don't know how many months she was a member of the first gym and how many months, out of a year, she was a member of the 2nd gym. Let's find out, let's call the number of months of the membership at 75 x and the months at 50 y:
x+y = 12 subtract x from both sides:
y = 12-x we'll use this value for y next:
75x+50y = 775 Now substitute for y:
75x+50(12-x)= 775
75x+600-50x = 775
25x = 175
x = 7 She paid 75 during 7 months and
12-7 = 5 months at 50
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Check:
7*75 = 525
5*50 = 250
_ _ _ -----
Total: 775 We have the correct answer
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Write a system of equations that corresponds to the situation.
- Lisa spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym and spends the rest of the year with the second gym. The membership to the first gym costs $75 per month, while the membership for the second gym costs $50 per month. She ends up spending a total of $775 over the course of the year.
Let number of months spent at 1st and 2nd gyms, be F, and S, respectively
We then get: 
Also, 
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