Fun Center rents popcorn machines for $20 per hour. In addition to the hourly charge, there is a rental fee of $32. Is the number of hours you rent the popcorn machine proportional to the total cost?

Please answer the question. I need help.

You need to put the number $20 in a line. You need to keep adding to see if it's proportional.

$20 + $32 = $52

Put it in like this: 20, 40, 60
That is 3 hours. Now add the '32' do the number. Divide them by 2. See if it's proportional.

It is not proportional. If it were, the relationship would look like

cost = 20 * hours
But this is not true, since your function is cost = 20 * hours + 32

Yes, the number of hours you rent the popcorn machine is proportional to the total cost.

To determine if the number of hours you rent the popcorn machine is proportional to the total cost, we need to compare the cost to the number of hours rented.

Let's break down the total cost formula:

Total Cost = Hourly Charge + Rental Fee

The Hourly Charge for renting the popcorn machine is given as $20 per hour. So, if you rent the machine for "x" hours, the Hourly Charge component of the total cost would be 20x.

The Rental Fee is a one-time charge of $32.

Therefore, the total cost can be represented as:

Total Cost = 20x + 32

Now, let's analyze if the number of hours rented is proportional to the total cost.

If the total cost is directly proportional to the number of hours rented, it means that if you double the number of hours, the total cost will also be doubled. Similarly, if you triple the number of hours, the total cost will triple, and so on.

Let's examine the cost for a few different scenarios:

1) Rented for 2 hours:
Total Cost = 20(2) + 32 = 40 + 32 = 72

2) Rented for 4 hours:
Total Cost = 20(4) + 32 = 80 + 32 = 112

3) Rented for 6 hours:
Total Cost = 20(6) + 32 = 120 + 32 = 152

By comparing these examples, we can see that the total cost is not directly proportional to the number of hours rented. If it was, each time the number of hours doubled, the total cost would also double. However, in the given examples, the total cost increased less than double when the number of hours doubled.

Therefore, we can conclude that the number of hours you rent the popcorn machine is not proportional to the total cost.