Maya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges and allows unlimited mileage.
Company B has an initial fee of and charges an additional for every mile driven.
For what mileages will Company A charge no more than Company B?
Use for the number of miles driven, and solve your inequality for
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Sra
Let x be the number of miles driven.
For Company A, there is a fixed price, so the cost C1 can be represented as:
C1 = A
For Company B, there is an initial fee and an additional charge per mile, so the cost C2 can be represented as:
C2 = B + C * x
We want to find the mileages for which Company A charges no more than Company B. In other words, we want to find the values of x for which C1 ≤ C2.
Substituting the expressions for C1 and C2, we have:
A ≤ B + C * x
To solve for x, we can isolate it on one side of the inequality:
A - B ≤ C * x
Dividing both sides by C (assuming C is positive), we have:
(A - B) / C ≤ x
Therefore, for mileages x greater than or equal to (A - B) / C, Company A will charge no more than Company B.
To compare the costs of renting a truck from Company A and Company B, we need to set up an inequality.
Let's say the number of miles driven is represented by "x".
For Company A, the cost is fixed, so it can be represented as a constant value, let's call it "c".
For Company B, the cost is a combination of an initial fee and an additional charge per mile driven. The initial fee is represented as "i", and the additional charge per mile driven is represented as "a". Therefore, the cost from Company B can be calculated as "i + ax".
To find the mileages where Company A charges no more than Company B, we need to set up the inequality:
c ≤ i + ax
Now, let's solve the inequality for "x".
Given the information in the problem, we don't know the specific values of "c", "i", and "a". However, we can use the given amounts to demonstrate how to solve the inequality.
Let's assume Company A charges $50 and Company B has an initial fee of $20 and an additional charge of $0.50 per mile driven:
50 ≤ 20 + 0.50x
To solve for "x", we can start by subtracting 20 from both sides of the inequality:
50 - 20 ≤ 0.50x
30 ≤ 0.50x
Next, we can divide both sides of the inequality by 0.50:
30 / 0.50 ≤ x
60 ≤ x
Therefore, for mileages equal to or greater than 60, Company A will charge no more than Company B.