a gas station has 30 gallon of gasoline worth 1.20 per gallon and some worth 1.40 per gallon .how many gallons of the 1.40 brand must the owner mix in to produce gasoline that cost 1.28 per gallon

Dominique, We can do this with with one gallon to begin with.

If we let x= the amount of the one gallon that is the $1.20/gal then 1-x is the amount of the $1.40/gl because x+(1-x)=1

1.2*x+(1-x)*1.4=1.28 solving this gives x=.6 gal and 1-x=.4 gal

You can now use these fractions to calculate the amount needed for any amount.

If you wanted to make up 30 gallons of $1.28 gas you would use .6*30 or 18 gal of 1.20 gas and .4*30 or 12 gal of the 1.40 gas

18*1.2=21.60

12*1.4=16.80

This totals up to 30 gallons and cost $38.40 and the cost per gallon is 38.40/30=1.28

Jim