Question

Yesterday Mike bought 2 gallons of regular gasoline and 3 gallons of premium gasoline at a gas station for $13.60 today he bought 3 gallons of regular gasoline and 4 gallons a premium gasoline for $18.95 if the prices do not change how much does one gallon of premium gasoline cost

Answer 1

Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.

Explanation:

Let the Cost of Regular gasoline be 'x'.

Let the Cost of Premium gasoline be 'y'.

Given:

Amount of regular gasoline bought yesterday = 2 gallons

Amount of premium gasoline bought yesterday = 3 gallons

Total Cost of yesterday = $13.60

Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.

Framing in equation form we get;

`2x+3y=13.60 \ \ \ \ equation\ 1`

Also Given:

Amount of regular gasoline bought today = 3 gallons

Amount of premium gasoline bought Today = 4 gallons

Total Cost of Today = $18.95

Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.

Framing in equation form we get;

`3x+4y=18.95 \ \ \ \ equation\ 2`

Now Multiplying equation 1 by 3 we get;

`2x+3y=13.60\\\\3(2x+3y)=13.60*3\\\\6x+9y= 40.80 \ \ \ \ \ equation\ 3`

Now Multiplying equation 2 by 2 we get;

`3x+4y=18.95\\\\2(3x+4y)=18.95*2\\\\6x+8y= 37.90 \ \ \ \ \ \ equation\ 4`

Subtracting equation 4 from equation 3 we get;

`(6x+9y)- (6x+8y)= 40.80-37.90\\\\6x+9y-6x-8y= 2.9\\\\y=\$2.90`

Substituting the value of y in equation 1 we get;

`2x+3y=13.60\\\\2x+3*2.90 =13.60\\\\2x+8.7=13.6\\\\2x=13.6-8.7\\\\2x=4.9\\\\x=(4.9)/(2) =\$2.45`

Hence Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.