```Question 96028
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) {{{C+20x = 52.90}}} ...and the sister's move.
2) {{{C+60x = 81.70}}}
Now you have two equations with two unknowns (C and x).
Rewrite these as:
1a) {{{C = 52.90-20x}}} and...
2a) {{{C = 81.70-60x}}}
But the flat rate, C, is the same in both cases, so equation 1a) is equal to 2a).
{{{52.90-20x = 81.70-60x}}} Simplify and solve for x, the cost per mile.
{{{52.90+40x = 81.70}}} Now subtract \$52.90 from both sides.
{{{40x = 28.80}}} Finally, divide both sides by 40 to get x.
{{{x = 0.72}}} 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:

{{{C = 52.90-20(0.72)}}} Simplify.
{{{C = 52.90-14.40}}}
{{{C = 38.50}}}...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..

{{{C+85x = 38.50+85(0.72)}}} = {{{38.50+61.20 = 99.70}}}
The cost of a one-day move of 85 miles is \$99.70

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