How many gallons of milk containing 4% fat must be mixed with milk containing 1% fat to obtain a 15 gallon mixture containing 2% fat?

Question

For the given problem, write a system of equations, clearly define any variables, and show all work.

Answer 1

Here is a summary of the milks you have and the one you want to create. We can use variables for the information we don't have (volume of milk). This helps us to keep in mind how we create the equations.

Milk 1 = 4% fat, x gal

Milk 2 = 1% fat, y gal

Milk 3 = 2% fat, 15 gal

You have two variables you need to find, which means you will need at least 2 equations. Then you can isolate one variable in one of the equations, and use that to solve the other equation.

Start off with what you know: You want a total of 15 gallons of combined milk 1 and milk 2.

x + y = 15

Now try to create another equation. You know that you want to have 2% fat in the 15 gallon mixed milk. The total amount of fat in the milk (in gallons) is 2% of the 15 gallons -> 2% x 15 = 0.02(15). We use multiplication to find a percent of something.

You can use the numbers and variables from the other milks to create an equation saying that the total amount of fat (percent multiplied volume) in those milks added together equals the total amount of fat in the final milk. Remember to use decimals!

x(0.04) + y(0.01) = 0.02(15) -> Here it helps to go ahead and multiply by 100 to simplify the values.

4x + y = 30

Now use equation one to solve equation 2 by isolating one of the variables (it doesn't matter which one). You can also do it the other way, just solve one of the equations for one isolated variable on one side, and the easier one is best.

x + y = 15

x = 15 - y -> plug this in for x in the second equation.

4(15-y) + y = 30

60 - 4y + y = 30

-3y = = -30

y = 10

If y = 10, you can find x by substituting the 10 into any equation.

x+ y = 15

x + 10 = 15

x = 5

Therefore you need 5 gallons of the 4% milk and 10 gallons of the 1% milk to create the 15 gallons of 2% milk.

You can check your answer by plugging both values into any equation

Answer 2

Hello Jordan,

Let x= # gallons of 4% fat milk.

Let y = # gallons of 1% fat milk.

x + y = 15 (gallons + gallons = gallons)

.04x + .01y = (.02)(15)

(%fat•gallons)+(%fat•gallons)=(%fat•gallons)

Many people like to multiply the second equation by 100 on both sides of the equation to clear the decimal points.

4x + 1y = 2•15 =30

Now solve the first equation for y: y = 15 - x.

Substitute this expression for y in the second equation.

4x + 1(15 - x) = 30

4x + 15 - x = 30

3x + 15 = 30

3x = 15

x = 5

Since x + y = 15, y = 10

It takes 5 gallons of 4% milk added to 10 gallons of 1% milk to equal 15 gallons of 2% milk

Regards,

Anita A.