Question

Algebra 2 E.11 Solve a system of equations using any method: word problems ELG You have prizes to Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Dakota is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $117. Dakota will be earning a base salary of $95 per month from the gym, plus an additional $11 for every class she teaches. If Dakota teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Dakota's expenses and earnings be? How many classes will that take? Dakota's expenses and earnings will both be $ once she teaches classes. Submit

Answer 1

Dakota needs to teach 2 classes to earn back her certification cost of $117. Her total earnings can be represented by E = 95 + 11x. By solving the equation E = 117 for x, the conclusion is that teaching 2 classes will make her expenses and earnings both equal $117.

Step-by-step explanation:

To solve this algebraic word problem, let's define our variables. Let x be the number of classes Dakota teaches in the first month. Dakota's total earnings can be represented by the equation E = 95 + 11x, where E is the total earnings, 95 is the base salary, and 11 is the additional amount she earns per class. She needs to earn back her certification cost, which is $117.

To find how many classes Dakota needs to teach to earn back her certification cost, we set up the equation E = 117. Substituting this into the earnings equation gives us 117 = 95 + 11x. Solving for x will give us the number of classes Dakota needs to teach to break even on her expenses.

Solving the equation 117 = 95 + 11x for x, we subtract 95 from both sides to get 22 = 11x, and then divide both sides by 11 to find that x = 2. Therefore, Dakota needs to teach 2 classes to earn back her certification cost.