Question 968792


let the cost of regular gasoline be  {{{p}}}, the cost of premium gasoline be {{{p[1]}}}

if the total cost of {{{10}}} gallons of regular gasoline and {{{15}}} gallons of premium gasoline is ${{{32.75}}}, then 

{{{10p+15p[1]=32.75}}}..........eq.1

if premium costs $.20 more per gallon than regular, then {{{p[1]=p+0.20}}}

The total cost is: 

{{{10p+15(p+0.20)=32.75}}}.....eq.2....solve for {{{p}}}

{{{10p+15p+3=32.75}}}

{{{25p=32.75-3}}}

{{{p=29.75/25}}}

{{{p=1.19}}}...=>the cost per gallon of regular gasoline


now find the price of premium


{{{p[1]=p+0.20}}}

{{{p[1]=1.19+0.20}}}

{{{p[1]=1.39}}}...=>the cost per gallon of premium gasoline


check:

the total cost of {{{10}}} gallons of regular gasoline is ${{{10*1.19=11.9}}}

and {{{15}}} gallons of premium gasoline is {{{15*1.39=20.85}}}

 then ${{{32.75=11.9+20.85}}}=> ${{{32.75=32.75}}}