SOLUTION: A moving company charges a certain flat rate per day, plus a per-mile charge. It charged your brother $52.90 for a one-day move of 20 miles. Your sister used the same company

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Question 96028: A moving company charges a certain flat rate per day, plus a per-mile charge. It charged your brother $52.90 for a one-day move of 20 miles. Your sister used the same company and was charged $81.70 for a one-day move of 60 miles. What would you predict to pay for a one-day move of 85 miles?
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
First, I would calculate the flat-rate cost (C) and the cost per mile (x). This can be done as follows:
Write the equation for the cost of the brother's move of $52.90 for a 20-mile move...
1) ...and the sister's move.
2)
Now you have two equations with two unknowns (C and x).
Rewrite these as:
1a) and...
2a)
But the flat rate, C, is the same in both cases, so equation 1a) is equal to 2a).
Simplify and solve for x, the cost per mile.
Add 60x to both sides.
Now subtract $52.90 from both sides.
Finally, divide both sides by 40 to get x.
So the cost per mile is 72 cents. Now that we have that, we can go back to either equation 1a) or 2a) to find the value of C, the flat-rate cost. Let's use equation 1a) and we;ll substitute x = $0.72:
Simplify.

...and this ($38.50) is the flat-rate cost.
Now we can work out the cost for a one-day move of 85 miles by using 1) but substituting C = $38.50 and x = $0.72 per mile..
=
The cost of a one-day move of 85 miles is $99.70