One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. to obtain a mixture of 60 gallons with an octane rating of 120, how many gallons should be used from the tank with the octane rating of 80?

Call x the volume of gas whose octane rating is 140 and y the volume of gas whose octane rating is 80, then:

(1) x*140 + y*80 = 60*120, and

(2) x + y = 60

from (1) 140x + 80y = 7200 = > (3) 7x + 4y = 360

from (2) - - - > (4) 4x + 4y = 240

Subtract (4) from (3)

7x - 4x = 360 - 240

3x = 120

=> x = 120/3 = 40

=> y = 120 - 40 = 80

Answer: should be used 80 gallons from tank with the octane rating of 80