Addition Method: blending 3%-fat yogurt w/ no-fat to get 1%

A

angel716

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I have this question: Ziggy's Famous Yogurt blends regular yogurt that is 3% fat with it's no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

(is this the formula) x+y=60
0.03x+0.01y(60+r)=60
0.03x+60-0.01=60
0.03x=0.02

0.02/0.03=.66
x=66 and y 60= 6 gallons

pls assist if there is an easier way to do this thanks
 
Re: Addition Method

angel716 said:
I have this question: Ziggy's Famous Yogurt blends regular yogurt that is 3% fat with it's no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

(is this the formula) x+y=60 <<< I don't know - you did not tell me what 'x' & 'y' stand for here.
0.03x+0.01y(60+r)=60 <<< What is 'r' here?
0.03x+60-0.01=60 <<< This step does not follow from above - explain.
0.03x=0.02

0.02/0.03=.66
x=66 and y 60= 6 gallons <<< I don't know what is being done here

pls assist if there is an easier way to do this thanks
Click to expand...

Let

Volume of High fat yogurt = H

Volume of Low fat yogurt = L = 60 - H ........................(1)

..........Given condition

0.03 * H + 0.0*(60 - H) = 60 * 0.01 ...........................(2)

0.03 * H = 6

Solve for 'H' from above and then solve for 'L' from (1)

Check your answer by putting back your calculated values into (1) and (2).
 
Re: Addition Method

I don't get that answer. I get 20 pounds.
This is what is called a "mixture" problem. I have found the key to solving these problems is to concentrate on one element of the mixture. In this case either choose the fat or choose the yogurt. For demonstration I will make up a similar problem.
You want to get 90 pounds of mixed nuts containing 10% almonds using a mixture of nuts with 15% almonds and another mixture containing no almonds. How many pounds of each do you use?
I will first concentrate on the almonds. I'm thinking the amount of almonds in the first batch + the amount of almonds in the second batch will equal the amount of almonds in the final mixture.
How many almonds in the first batch?
The first thing we have to do is name things so we can talk about them. Let's name the number of pounds in the first batch as x. What do we name the number of pounds in the second batch? I could use a second variable and call it y. Then I know that x+y=90. Or, instead of naming it y, I could name the second batch 90-x. That's what I'll do. I write it down.
Let the number of pounds of almonds in the first batch be named x.
The number of pounds of almonds in the second batch is named 90-x.
Now to build an equation based on the idea that the number of pounds of almonds that we start with will be the same as what we end up with.
The number of pounds of almonds in the first batch is 15% of x or 0.15x.
The number of pounds of almonds in the second batch is 0.
The number of pounds of almonds in the final mixture is 10% of 90 or 9.
Therefore we can build the equation 0.15x + 0x = 9.
We solve that for x, getting x=60 lbs. etc.

If we would have concentrated on the "non-almond" portion of the mixture we would have gotten the equation
.85x + 1.00(90-x) = .90(90)
I think you get the same results.
I hope you will study what has been done so you understand the concept involved. That should solve your problem.
 
Re: Addition Method

thank you loren for breaking into a different perspective with same concept (if you get my meaning) I was attempting to use the example in the book however it seems that i have just confused my self even more with trying to use it...your nuts example is great thank you..the other example will work on it but i still didn't understand. I just want you to know its not you its me, I shouldn't even be in int algebra but my college will not let me in to a lower class...I am an absoluate horror at this....thanks again
 
Re: Addition Method

mmm my counslor just advised me that there is nothing lower at the university of phoenix other than this class I know for darn sure I shouldn't be in this class, but hes says as long as I pass with a D I should be fine..I get the equation a lil bit and even attempted the example that loren gave me however still can't wrap my head around and yes the class if paid for through grants and loans so yeah....*sheepishly*
 
angel716 said:
… my counslor just advised me that there is nothing lower at the [University] of [Phoenix] …
Click to expand...


OIC.

Your first statement says something else.

 
>but hes says as long as I pass with a D I should be fine..

Terrible advice. That counselor should be fired. A D is just a polite F and says you really don't understand. I'm asking "why take the course if you don't gain anything from it?" My advice would be to go to your local community college or adult school for a first course in Algebra. Then, take the Intermediate Algebra course next semester.
 
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