How much of a 40% antifreeze solution must a mechanic mix with an 80% antifreeze solution if 20 gallons of a 50% antifreeze solution are needed.

Question

How much of a 40% antifreeze solution must a mechanic mix with an 80% antifreeze solution if 20 gallons of a 50% antifreeze solution are needed.

Answer 1

Quantity of 40% antifreeze solution = x

Quantity  80% antifreeze solution=y

 

x + y = 20  -----------> x= 20-y

 

0.4x + 0.8y = 20(0.5)

 

0.4(20-y) + 0.8y = 10

 

8 -0.4y +0.8y =10

8+0.4y =10

0.4y =2

y=5

 so x =20-5=15

Quantity of 40% antifreeze solution = x = 15 gallon
Quantity 80% antifreeze solution=y = 5 gallon