Find how many quarts of 6?% butterfat milk and 3?% butterfat milk should be mixed to yield 30 quarts of 5?% butterfat milk.

Question

i need help in the next 20 mins please help me

Answer 1

This is a weighted averages problem; normally, you find the average by adding up all the numbers and dividing the total by the number of quantities you added up:

 

(X + Y + Z) / 3 = Average

 

Thanks to the distributive property, I can divide each value by 3:

 

X/3 + Y/3 + Z/3 = Average

 

Each piece (X, Y, and Z) gets an equal share in composing the average. They each get one third or 33% of creating the final average. In this problem, the 6% butterfat milk and the 3% butterfat milk, don't have an equal percentage in making the 5% milk. I will set up the problem like so:

 

(percentage of contribution from 6% milk)(6% milk) + (percentage of contribution from 3% milk)(3% milk) = 5% milk

 

Now, how do I find out how much of a contribution each milk will make?

 

I know that there will be 30 quarts of milk in all, so....

 

(quarts of 6% milk) + (quarts of 3%) = 30

 

Now, I will call the quarts of 6% milk X

I will call the quarts of 3% milk Y

 

(quarts of 6% milk) + (quarts of 3%) = 30

             X               +         Y            = 30

 

I know that 30 is the total amount of quarts. To find how much "weight" each milk has in computing the average, I can take each amount of milk and divide it by the total amount of milk:

 

(contribution from 6% milk) = X/30

(contribution from 3% milk) = Y/30

 

As fractions, these numbers represent how much weight each milk will have in computing the average.

 

X/30(6% milk) + Y/30(3% milk) = 5% milk

 

Now, in order to do the necessary math, I need to convert all percentages into decimals

 

X/30(0.06) + Y/30(0.03) = 0.05

 

Since both the X and the Y are being divided by 30, I can multiply both sides of the equation by 30:

 

X(0.06) + Y(0.03) = 0.05*30 (which equals 1.5)

 

Now, we still have two unknown numbers. I can get rid of one of them by using our other equation:

 

X + Y = 30 (because the total number of quarts will equal 30)

 

and I can simply rearrange it thus:

 

X = 30 - Y

 

And I can substitute 30 - Y in for X:

 

(30 - Y)(0.06) + Y(0.03) = 1.5

 

This is what Mark set up for you; just solve for the amount of 3% milk and then find the amount of 6% milk.

:)

 

Answer 2

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Answer 3

x represents amount of 3%

0.06(30 - x) + 0.03x = 0.05(30)

1.8 - 0.06x + 0.03x = 1.5

1.8 - 0.03x = 1.5

-0.03x = -0.3

x = 10