Question

Tom wants to join a gym. Gym A charges a $150 membership fee plus $50 per month. Gym B charges an $80 membership fee plus $75 per month. Write and graph a system of equations to determine when the cost at both gyms is the same. Define variables for the unknowns. Also, Make a graph to represent this situation.

Answer 1

Step-by-step explanation:To determine when the cost at both gyms is the same, let's define variables for the unknowns.

Let's use:

- "x" to represent the number of months

- "C_A" to represent the cost at Gym A

- "C_B" to represent the cost at Gym B

For Gym A, the cost is the sum of the membership fee and the monthly fee, which is $150 + $50x.

For Gym B, the cost is the sum of the membership fee and the monthly fee, which is $80 + $75x.

To find when the costs at both gyms are the same, we need to solve the equation:

$150 + $50x = $80 + $75x

Now, let's graph the system of equations to represent this situation. The x-axis will represent the number of months, and the y-axis will represent the cost.

On the graph, plot the line for Gym A using the equation C_A = $150 + $50x. This line will have a y-intercept of $150 and a slope of $50. Connect the points on the graph to form the line.

Next, plot the line for Gym B using the equation C_B = $80 + $75x. This line will have a y-intercept of $80 and a slope of $75. Connect the points on the graph to form the line.

The point where the two lines intersect represents the number of months when the costs at both gyms are the same. Label this point on the graph.

To summarize:

- The equation for Gym A is C_A = $150 + $50x

- The equation for Gym B is C_B = $80 + $75x

- The point where the two lines intersect represents when the costs at both gyms are the same.

Remember, this is a visual representation, and you can use the graph to determine the number of months when the costs at both gyms are equal.

Answer 2

A system of linear equations is created to find when the cost of Gym A and Gym B are equal. The equations are based on the fixed membership fee and the monthly fee for each gym, which are then graphed to find the intersection point.

Step-by-step explanation:

To determine when the cost at both Gym A and Gym B is the same, we need to create two linear equations based on the information provided:

• Let x represent the number of months of gym membership.
• Gym A's cost can be represented as y = 150 + 50x (where 150 is the membership fee and 50 is the monthly fee).
• Gym B's cost can be represented as y = 80 + 75x (where 80 is the membership fee and 75 is the monthly fee).

To graph these equations, plot the y-intercept for each line (150 for Gym A and 80 for Gym B) and use the slope to determine the points to connect for the lines. The intersection point of the two lines is where the costs are the same.