SOLUTION: Hi appreciated tutors, I have been studying linear systems and have a good understanding of solving them but this word problem is driving me crazy. Here is the problem verbatim;

Question 968792: Hi appreciated tutors,
I have been studying linear systems and have a good understanding of solving them but this word problem is driving me crazy. Here is the problem verbatim;
The total cost of 10 gallons of regular gasoline and 15 gallons of premium gasoline is $32.75. Premium costs $.20 more per gallon than regular. What is the cost per gallon of each type of gasoline?
I tried to set up the problem like this:
x+y=25
10x+15y=32.75
I figured the .20 would be added to the final "y" value.
The way it comes out when I work the equations by trying to use substitution is a negative number. This is one indication I am working it incorrectly. Please show me a verbal model and work the equations and explain how to include the".20". THANKS very much!

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The total cost of 10 gallons of regular gasoline and 15 gallons of premium gasoline is $32.75. Premium costs $.20 more per gallon than regular. What is the cost per gallon of each type of gasoline?
=================
10R + 15P = 3275
P = R + 20
----------------
Sub for P
10R + 15*(R+20) = 3275
25R + 300 = 3275
R = 119
P = 139
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

let the cost of regular gasoline be , the cost of premium gasoline be
if the total cost of gallons of regular gasoline and gallons of premium gasoline is $, then
..........eq.1
if premium costs $.20 more per gallon than regular, then
The total cost is:
.....eq.2....solve for

...=>the cost per gallon of regular gasoline

now find the price of premium

...=>the cost per gallon of premium gasoline

check:
the total cost of gallons of regular gasoline is $
and gallons of premium gasoline is
then $=> $

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