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?

Answer 1

When dealing with mixture problems a table is very helpful! I've created one for you:

Type of milk	# of gallons	Total
4% fat	x	.04x
1% fat	15-x	.01(15-x)
2% fat	15	.02(15)

Now to get the # of gallons, we are trying to find how much 4% fat we need so we make that x. For the gallons of 2% the problem says we need 15 gallons. So to find the number of 1% gallons, we subtract our 4% gallons from the total 15 gallons which gives us the expression "15-x". To get the total column, we multiply across the rows. Be sure to change your percents to decimals (ex: 4% = .04).

Now we know we add our 4% and 1% to equal the 2% so we can add our expressions in the total columns and set them equal to the 2%, simplify, and solve:

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

.04x + .15 - .01x = 0.3

.03x + .15 = 0.3

-.15 -.15

.03x = .15

/.03 /.03

x = 5

So, we would need 5 gallons of the 4% fat milk. I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to comment or reach out to me. Learn on! :)