Question

Using Substitution to Solve a System of Equations
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Upcharges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.

y = 7.5x

y = 5.5x + 10

1. Substitute: 7.5x = 5.5x + 10

How many classes could Anna take so that the total cost for the month would be the same?

______classes

What is the total monthly cost when it is the same for both gyms?

$_____

Answer 1

The answer is c

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Answer 2

Given:

Equations representing the costs of the two gyms:

y = 7.5x

y = 5.5x + 10

To find:

1. Number of classes Anna could take so that the total cost for the month would be the same

2. The total monthly cost when it is the same for both gyms

Solution:

We can find the solution to the above problem by following the given steps-

1. We know that for the total cost to be equal for both the months, the equations representing costs would also be equal.

Equation of cost of Fit Fast, y = 7.5x

Equation of cost of Stepping Up, y = 5.5x + 10

If both the costs are equal, the values of y would also be equal.

7.5x= 5.5x+ 10

7.5x-5.5x=10

2x=10

x=5

So, Anna could take 5 classes at both gyms for the monthly cost to be equal.

2. The total monthly cost when it is the same for both the gyms can be obtained by substituting the value of x in the equation.

For Fit Fast, the cost when x=5 is

y=7.5×5

y= $37.5

For Stepping up, the cost when x=5 is

y=5.5×5 +10

y= 27.5+10

y= $37.5

The total monthly cost is $37.5

Therefore, Anna can take 5 classes so that the total cost for the month would be $37.5.