Jan 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 wit

Question

3 years ago

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Jan 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 wit

h the first gym after x months and spends the rest of the year, y months, with the second gym. The membership to the first gym costs $75 per month, while the membership for the second gym costs $45 per month. If she ended up spending a total of $780 over the course of the year, how much time did she spend at each gym?
Enter a system of equations to represent the situation.

Mathematics

1 answer:

valkas [14] · Answer 1 · 2022-05-18T04:34:46+03:00

She spent 8 months in the 1st gym and 4 months in the 2nd gym

Step-by-step explanation:

Jan 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 after x months
She spends the rest of the year, y months, with the second gym
The membership to the first gym costs $75 per month, while the membership for the second gym costs $45 per month
She ended up spending a total of $780 over the course of the year

We need to find how much time she spent at each gym

∵ She spent x months in the 1st gym

∵ She spent y months in the 2nd gym

∵ Her course is a year

- There are 12 months in a year

∴ x + y = 12 ⇒ (1)

∵ The membership to the first gym costs $75 per month

∵ The membership to the second gym costs $45 per month

∵ She ended up spending a total of $780 over the course

∴ 75x + 45y = 780 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -45 to eliminate y