Gasoline mixture question

Question

A service station has 65 octane and 78 octane gasoline. How many liters of each gasoline should be mixed to provide 13 liters of 75 octane gasoline for a chemistry experiment?

Answer 1

Let X = liters of 65 octane gasoline

Let Y = liters of 78 octane gasoline 

 

13 liters  ==>  X + Y = 13 ==>  Y = 13 - X

 

To get 13 liters of 75 octane gasoline will require X liters of 65 octane gasoline and (13 - X) liters of 78 octane gasoline to add up to 13 * 75 

 

65*X + (13 - X)*78 = 75 * 13

65*X + 1014 - 78*X = 975

-13*X = -39

X = 3 

 

So Y = 13 - 3 = 10 

 

There should be 3 liters of 65 octane gasoline and 10 liters of 78 octane gasoline 

 

Check:  3*65 + 10*78 = 195 + 780 = 975, and 975/13 = 75