Question

How many gallons of 20% alcohol solution and a 60% alcohol solution must be mixed to get 16 gallons of 30% alcohol solution

Answer 1

The number of gallons of 20% alcohol solution is 12 and the number of gallons of 60% alcohol solution is 4

Explanation:

Let

x ----> the number of gallons of 20% alcohol solution

y ----> the number of gallons of 60% alcohol solution

we know that

20%=20/100=0.20

60%=60/100=0.60

30%=30/100=0.30

x+y=16

x=16-y ------> equation A

0.20x+0.60y=16(0.30) ------> equation B

Solve by substitution

Substitute equation A in equation B and solve for y

0.20(16-y)+0.60y=16(0.30)

3.2-0.20y+0.60y=4.8

0.40y=4.8-3.2

0.40y=1.6

y=4 gal

Find the value of x

x=16-y

x=16-4=12 gal

therefore

The number of gallons of 20% alcohol solution is 12 and the number of gallons of 60% alcohol solution is 4