Answer:
Explanation:
Hey! Let's help you with your question there!
To start, we want to know an equation that models this problem. Well, what do we know exactly? Let's take a look at what we know!
So what do we know? We know for a fact that the rental company charges an initial fee of $43 with an additional fee per hour. So far, this is the only thing we have going for us. However, I can see in the question that you managed to figure out what the hourly fee was, which, in our case, is perfect!
Now that we have that information, we can begin to model our equation for this problem. To model this equation, we are not looking for anything specific. We want this equation to be able to represent how much it'll cost in total for how long Stefan's family rents the rototiller. From this, let's take a look at what is our fixed costs and our variable costs.
When we talk about fixed costs, I am referring to a number that won't change no matter what. This specific problem refers to a price where no matter how many hours Stefan's family rents the rototiller, it will always be a cost added to our calculation. In this case, the rental company charges an initial fee of $43. Meaning that regardless of how many hours they rent it for, they will always have to pay the $43 to use it.
Now, we get onto variable costs. What I'm referring to here is the number that changes either due to quantity or time. In this problem, we have a number that changes due to time. Here, you have already solved that the hourly rate is $3 an hour. This means that depending on how long it is rented for, it will go up $3 for every hour. And from here, we have everything we need!
The Equation!
Now, why is it like this? We'll let y represent the total cost.
represents $3 for however many hours they've rented the rototiller for. 43 represents the initial fee they have to pay in order to use the rototiller.
Checking our work!
We can check if this works by substituting part of the question into the formula. Now, in the second half of the question, we know that the total paid was $64. Not only that, we also know they rented the rototiller for 7 hours. Let's pretend for a moment that we don't know the total is $64. If we substitute 7 hours into our equation, we get:
-Our equation we came up with.
- Substituting 7 hours into h.
- 7 multiplied by 3 = 21.
- 21 plus 43 = 64.
In the end, we do in fact end up getting our total of $64, which we knew from the start! This means that this equation works as intended!
If there are any further questions, please leave a comment, and I will respond to it the best I can.