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
∵ -45x - 45y = -540 ⇒ (3)
- Add equations (2) and (3)
∴ 30x = 240
- Divide both sides by 30
∴ x = 8
- Substitute the value of x in equation (1) to find y
∵ 8 + y = 12
- Subtract 8 from both sides
∴ y = 4
She spent 8 months in the 1st gym and 4 months in the 2nd gym
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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