Question

suppose you have 1000 gallons of gasoline 20% is premium and 80% is regular how much premium gas needs to be added to bring the mixture to 60% premium​

Answer 1

20% of 1000 gal = 200 gal of premium gasoline

80% of 1000 gal = 800 gal of regular gasoline

x = volume of premium gasoline that you need to add to the current mixture

60% of the new mixture is supposed to be premium gasoline. The new mixture would have a total volume of (1000 + x) gal, and in this total, you'd have (200 + x) gal of premium gasoline. So

$\dfrac{200+x}{1000+x}=0.60\implies200+x=600+0.60x$

$\implies400=0.40x\implies x=1000$

You'd need to add 1000 gal of premium gasoline to get a mixture of 60% premium.