Question

Five Seconds of Summer’s tutoring service charges a base charge of $5 and $5 per hour.

Fall Out Boy’s tutoring service charges a base fee of $9 and $3 per hour. Whose service
would you rather use?

Make a table for your system of equations. Highlight the shared point in your table.
Solve your system graphically. Label your solution on the graph.
Solve the system, algebraically using substitution. Solve for both variables and box in your answers.
Choose your response to the would you rather question. Provide evidence and math to back up your choice. Could there be a scenario in which you would pick another option and tell me your other option

Answer 1

To compare the costs of the two tutoring services, we can set up a system of equations. Let x be the number of hours of tutoring.

Five Seconds of Summer's tutoring service:

y = 5 + 5x (base charge of $5 and $5 per hour)

Fall Out Boy's tutoring service:

y = 9 + 3x (base fee of $9 and $3 per hour)

We can make a table to compare the costs of the two services at different number of hours:

Hours (x) Five Seconds of Summer (y) Fall Out Boy (y)

0 5 9

1 10 12

2 15 15

3 20 18

4 25 21

The shared point in the table is when x = 0, y = 5 for Five Seconds of Summer's tutoring service and y = 9 for Fall Out Boy's tutoring service.

We can graph the two equations to compare the costs:

[Graph would be here if I were able to create one]

From the graph we can see that for any number of hours greater than 0, Five Seconds of Summer's tutoring service is cheaper.

We can also solve the system algebraically using substitution.

y

Answer 2

Answer: The cost of both services is equal when h = 2 hours.

Step-by-step explanation: The shared point on the table is when the cost of the two services is equal, i.e. when C1 = C2, where C1 is the cost of Five Seconds of Summer's service and C2 is the cost of Fall Out Boy's service.

To graphically solve the system, we can plot the two equations on the same coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x

We can then find the point of intersection of the two lines, which represents the point at which the cost of the two services is equal. We can label this point as (x, y) and our solution.

To solve the system algebraically using substitution, we can set C1 = C2 and solve for the number of hours (h) in terms of cost.

C1 = 5 + 5h = C2 = 9 + 3h

5 + 5h = 9 + 3h

2h = 4

h = 2

So, the cost of both services is equal when h = 2 hours.

From the above result, it is clear that Fall Out Boy's service is cheaper than Five Seconds of Summer's service. For 2 hours of tutoring, the cost of Fall Out Boy's service is $9 + 3(2) = $15 and the cost of Five Seconds of Summer's service is $5 + 5(2) = $15.

However, there could be scenarios where one service is cheaper than the other depending on the number of hours of tutoring required. For example, if a student requires more than 4 hours of tutoring, Five Seconds of Summer's service would be cheaper. And if a student requires less than 2 hours of tutoring, Fall Out Boy's service would be cheaper.

In conclusion, the best option would depend on the number of hours of tutoring required, and it is best to check both options and compare the cost before making a decision