Applications of Systems of Linear Equations

Question

At ice rinks A and B, there is a cost for admission plus an hourly rate for skate rental.

1. Hours Rented 1 5 Rink A Cost ($):1935 Rink B Cost ($)1539

How many more dollars does it cost per hour to rent skates at Rink B than at Rink A?

Answer 1

*I am not sure this question is copied correctly due to the inconsistency with the answer request. However, the formula/steps would be the same regardless. You would just apply different numbers in your equations. I'll work you through the process using the stated data above.

To begin, you need to determine the costs of the two ice rinks in two different equations.

1. First, you have Ice Rink A where it costs 1935 to skate for 15 hours.
2. Then, you have Ice Rink B where it costs 1539 to skate for 15 hours.

Now you need to try to figure out your equations. Since it's a linear equation, we start with the standard linear form of y = mx + b. Now, we need to determine what each variable stands for in this problem

1. y = costs
2. m = slope or rate of change (or in this case) how much it costs per hour
3. x = numbers of hours skating (the independent variable)
4. b = would be the constant variable or the cost of the admission, which based on the data is the same.

Next, you'll want to write your two equations

1. Ice Rink A: 1935 = 15(m) + b
2. Ice Rink B: 1539 = 15(m) + b

Unfortunately, due to the incomplete question, this is where the problem would end. However, if you have the data in the original question, you would subtract the cost of admission (b) from both sides. From there, you would divide the cost by the numbers of hours (15). This will give you the cost per hour for each of the Ice Rinks.