SOLUTION: Two Gasoline Distributors, A & B, are 228 mi apart on Interstate 80. A charges $0.85/gal and B charges $0.80/gal. Each charges $0.05/gal per mile for delivery. Where on Interstate

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Question 144948This question is from textbook Basic Technical Mathmatics with Calculus
: Two Gasoline Distributors, A & B, are 228 mi apart on Interstate 80. A charges $0.85/gal and B charges $0.80/gal. Each charges $0.05/gal per mile for delivery. Where on Interstate 80 is the cost to the customer the same? This question is from textbook Basic Technical Mathmatics with Calculus

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=miles that A must drive to deliver gas at same price as B's
Then 228-x=miles that B must drive to deliver gas at the same price as A's
Cost of A's gas to the customer = 0.85/gal+0.05x
Cost of B's gas to the customer=0.80/gal+0.05(228-x)
Now we are told that the above costs must be the same, so:
0.85+0.05x=0.80+0.05(228-x) get rid of parens (distributive law)
0.85+0.05x=0.80+11.4-0.05x add 0.05x to and subtract 0.85 from each side
0.85-0.85+0.05x+0.05x=0.80+11.4-0.85-0.05x+0.05x collect like terms
0.10x=11.35 divide each side by 0.10
x=113.5 mi-------------------from A's distribution point
0r
228-x=228-113.5=114.5 mi--------------from B's distribution point
CK
0.85+0.05*113.5=0.80+0.05*114.5
0.85+5.675=0.80+5.725
6.525=6.525

Hope this helps----ptaylor