Question is in the description (IXL question)

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Winston is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, he spent a total of $65. Winston will be earning a base salary of $58 per month from the gym, plus an additional $7 for every class he teaches. If Winston teaches a certain number of classes during his first month as an instructor, he will earn back the amount he spent on certification. How much will Winston's expenses and earnings be? How many classes will that take?

Winston's expenses and earnings will both be $ once he teaches  classes.

Answer 1

Hi Dieg,

I'd be happy to help!

Variables:

1. E for Winston's total earnings.
2. C for the number of classes he teaches.

Equations:

1. Expenses: Winston spent 65 dollars on certification.
2. E_expenses = 65
3. Earnings: Winston earns 58 dollars per month plus 7 dollars for each class.
4. E = 58 + 7C

Objective:

1. Find the number of classes C Winston needs to teach to break even.

Solution:

1. Set the Earnings equation equal to the Expenses equation.
2. 65 = 58 + 7C
3. Solve for C.
4. C = 1

Interpretation and Further Exploration:

1. Winston will break even—his expenses and earnings will both be 65 dollars—when he teaches just one class.
2. Given that he only needs to teach one class to break even, Winston could potentially accumulate a significant profit if he teaches multiple classes per month.
3. This calculation assumes that the 58-dollar base salary is guaranteed irrespective of the number of classes he teaches. If this base salary has conditions attached, the break-even point might change.
4. It might also be beneficial for Winston to consider other costs, like commuting or equipment, to get a more comprehensive view of his profits and losses.
5. If Winston aims for a certain profit margin or wants to recoup his initial costs within a specific timeframe, he could set targets based on these calculations.

Let me know if you have any further questions! Or, if you find this helpful, I would greatly appreciate your feedback - it is incredibly helpful since I am considered new on this platform :)

Thanks,

Ben

Answer 2

65 < 58 + 7c, where c represents the number or classes necessary

Can you solve for c and answer?