A certain car ideally requires an engine oil which is composed of 90.50% base oil and the rest in additives. How many gallons of 84.00% engine oil and how many gallons of 96.00% engine oil must be combined to produce 50.00 gallons of 90.50% engine oil?
Let x be the number of gallons of 84.00% engine oil.
So, 50 - x is the number of gallons of 96.00% engine oil.
The equation that represents the amount of base oil in the final mixture is:
0.845x + 0.96(50 - x) = 0.905(50)
0.845x + 48 - 0.96x = 45.25
-0.045x = -2.75
x = 61
So, 61 gallons of 84.00% engine oil and 50 - 61 = <<50-61= -11>> 11 gallons of 96.00% engine oil must be combined to produce 50.00 gallons of 90.50% engine oil. Answer: \boxed{61}.