Math word problem

Question

How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?

Gallons of Solution,Percent (as a decimal)],[Gallons of Pure Alcohol

x 15%=0.15

y 10%=0.1

5 13%=

How many gallons of 15% alcohol should be in the mixture?

How many gallons of 10% alcohol should be in the mixture?

Answer 1

Hello Freddy,

One way to solve this is to create a system of 2 equations. First, you would need to complete the table.

For each solution: gallons of alcohol = gallons of solution * percent alcohol.

Gallons of Solution ,Percent (as a decimal)], [Gallons of Pure Alcohol

x 15%=0.15 0.15*x

y 10%=0.1 0.1*y

5 13%= 0.13 0.13*5 = 0.65

One equation will be about the gallons of each solution:

x + y = 5 (Let's call it Equation #1)

The other one will be for gallons of pure alcohol :

0.15*x + 0.1*y = 0.65 (Let's call it Equation #2)

You now have 2 equations with 2 variables x and y:

x + y = 5

0.15*x + 0.1*y = 0.65

You can multiply the second equation by -10:

x + y = 5

-1.5*x - 1*y = -6.5

Add both equations together to eliminate the y variable:

-0.5*x = -1.5. Divide both sides by -0.5 to get x: x = 3; that means 3 gallons of 15% alcohol should be in the mixture.

Now replace x by 3 in the equation #1: x+y = 5, so 3+ y = 5, all you have to do is solve for y and that will tell you how many gallons of the 10% alcohol should be in the mixture :)

Cheers.