word problems

Question

a truck can be rented from company A for $80 a day plus $0.50 per mile. company B charges $60 a day plus $0.90 per mile To rent the same truck. Find the numblr of miles in a day at which the rental costs for company A and company B r the same

Answer 1

The first step to solving this problem is to determine the 2 equations we will be using. These equations will use x as the unknown, which in this case is the number of miles. That would be as follows:

Company A- A=80+0.50x (The company charges a flat fee of 80 + 0.50 per mile)

Company B- B=60+0.90x (The company charges a flat fee of 60 + 0.90 per mile)

 

Next, we need to set the equations equal to one another because we want to know when the total charge from both companies will be the same.

So:  80+0.50x=60+0.90x

Solve for x. We do this by combining the x's on both sides, subtracting the smaller number from the larger to avoid negative numbers.

80+0.50x=60+0.90x    (subtract 0.50x from 0.90x)

80=60+0.40x.  (subtract 60 from 80)

20=0.40x     (divide by 0.40)

50=x

 

We can check our work by replacing the x in both equations with our answer: 50

80 + 0.50x= 60+ 0.90x

80 + 0.50 (50)=60+0.90 (50)

80+25=60+45

105=105

So our answer is 50 miles.

Hope this helps! 

Answer 2

Tabitha

 

for company A

C = 80+0.50m

 

For company B

C = 60+0.9m

 

80+0.5m = 60+0.9m

20=.4m

m=50 miles per day is the breakeven point

Answer 3

The basic requirement is that the Cost for renting from Company A = Cost for renting from Company B, right?

 

In this case there are two parts to the cost: Cost = (Days driven)(rental time Unit rate) + (miles driven)(mileage Unit rate).  The thing to also consider is that we'll need to work with 1 day of rental time to find the miles driven during that rental time: "a day."  The miles driven will have to be the same regardless of which company we end up going with, otherwise one company's total bill will be bigger or smaller than the other.

 

So with all the units in: 

(1day)($80/day) + x($0.50/mile) = (1day)($60/day) + x($0.90/mile)

OR without all the units:

0.5x + 80 = 0.9x + 60

 

You should be able to take it from here to solve for x.  If you're not sure of the answer you get, plug it into the original equation to see if it makes it true.  Hope that helps!