SOLUTION: A dairy farmer wants to mix a 55% protein supplement and a standard 25% protein ration to make 1200 pounds of a high-grade 45% protein ration. How many pounds of each should he use

Question 1152731: A dairy farmer wants to mix a 55% protein supplement and a standard 25% protein ration to make 1200 pounds of a high-grade 45% protein ration. How many pounds of each should he use?
Found 3 solutions by josmiceli, MathTherapy, greenestamps:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = pounds of 55% mix needed
Let = pounds of 25% mix needed
------------------------------------------------
(1)
(2)
----------------------------------------
(2)
(2)
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(2)
------------------------------

and
(1)
(1)
(1)
----------------------------
800 pounds of 55% mix are needed
400 pounds of 25% mix are needed
----------------------------------------
check:
(2)
(2)
(2)
(2)
(2)
OK
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

A dairy farmer wants to mix a 55% protein supplement and a standard 25% protein ration to make 1200 pounds of a high-grade 45% protein ration. How many pounds of each should he use?

Let amount of 55% protein be F
Then amount of 25% protein = 1,200 - F
We then get: .55F + .25(1,200 - F) = .45(1,200)
.55F + 300 - .25F = 540
.55F - .25F = 540 - 300
.3F = 240
F, or amount of 55% protein to use =
Amount of 25% protein to use =
That's IT!! Nothing that COMPLEX or LENGTHY!!
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Certainly if you are going to use a formal algebraic method to solve the problem you should use a single variable; the amount of work you need to do will be much less than if you use two variables.

Or here is a non-algebraic method that requires far less effort than the single variable algebraic method.

Consider the three percentages on a number line; specifically, look at where the 45% of the mixture lies in relation to the 25% and 55% of the two ingredients.
25 -------------- 45 ------- 55

Using any number of possible different calculations, find that 45% is two-thirds of the way from 25% to 55%.

That means 2/3 of the mixture needs to be the 55% ingredient.

ANSWER:
55% protein supplement: 2/3 of 1200 pounds, or 800 pounds
standard 25% protein ration: 1/3 of 1200 pounds, or 400 pounds

RELATED QUESTIONS
A dairy farmer wants to mix a 55% protein supplement and a standard 15% protein ration... (answered by josgarithmetic)
A dairy farmer wants to mix a 55% protein supplement and a standard 25% protein ration to (answered by josgarithmetic)
A dairy farmer wants to mix a 20% protein supplement and a standard 10% protein... (answered by josgarithmetic,ikleyn)
A dairy farmer wants to mix a 55% protein supplement and a standard 30% protein ration to (answered by mananth)
A dairy farmer wants to mix a 80% protein supplement and a standard 20% protein ration to (answered by Alan3354)
A dairy farmer wants to mix a 75% protein supplement and a standard 25% protein ration to (answered by mananth)
A dairy farmer wants to mix a 85% protein supplement and a standard 10% protein ration to (answered by jorel1380)
A dairy farmer wants to mix a 70% protein supplement and a standard 20% protein ration to (answered by Boreal)
A dairy farmer wants to mix a 45% protein supplement and a standard 20% protein... (answered by mananth,josgarithmetic,greenestamps)