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?
no - that fixed fee of $32 wrecks the proportion.
lmao, ofc it isnt proportional
fun center rents popcorn machines for $20 per hour.in addition to the hourly charge there is a rental fee of $35
No
Answer no
To determine whether the number of hours you rent the popcorn machine is proportional to the total cost, we need to look at the relationship between the number of hours and the total cost.
Let's denote the total cost as "C" and the number of hours as "h". According to the information given, there is an hourly charge of $20, as well as a rental fee of $32.
The total cost can be expressed as:
C = hourly charge + rental fee
Substituting the values, we have:
C = 20h + 32
This is a linear equation, of the form C = mx + b, where "m" represents the hourly charge (slope) and "b" represents the rental fee (y-intercept).
If the number of hours is proportional to the total cost, then the ratio of C to h should remain constant. Let's check by calculating the ratios for different values of h.
When h = 1 hour:
C = 20(1) + 32 = 52
Similarly, if we rent the popcorn machine for 2 hours:
C = 20(2) + 32 = 72
If we rent the popcorn machine for 3 hours:
C = 20(3) + 32 = 92
The ratios of C to h are:
52/1 = 52
72/2 = 36
92/3 ≈ 30.67
From the ratios calculated above, we can see that the ratio of C to h is not constant. Therefore, the number of hours you rent the popcorn machine is not proportional to the total cost.