mixture math problem

Question

A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?

first brand? ------ gallons?

Second brand? ------- gallons?

Answer 1

Let a = number of gallons of the 35% antifreeze and let b = the number of gallons of the 85% anitfreeze

Then a + b = 60

and (35a + 85b)/(a + b) = 45 from this equation we get 35a + 85b = 60(45) = 2700 & repeating

a + b = 60 or 35a + 35b = 60(35) = 2100

Solving the equations together, we find that b = 12 and a = 48