Here's my question:

Question

Here's my question:

Deep Thought Granola is 25% nuts and dried fruit. Oat Dream Granola is 10% nuts and dried fruit. How much of Deep Thought and how much of Oat Dream should be mixed to form a 20-lb batch of granola that is 19% nuts and dried fruit?

Here is a past question and the answer I got:
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Posted by Valeria on Friday, February 20, 2009 at 5:26pm.

The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 50-lb mixture that sells for $5.70 per pound?

c = lbs of cashews
b = lbs of brazil nuts

Are these the right equations?

b + c = 50

6.75b + 5c = 5.70

Thanks,
<3 Valeria <3

Responses

Algebra - Reiny, Friday, February 20, 2009 at 6:55pm
You are so close, or maybe it was just a typo.

Your last equation should have been

6.75b + 5c = 5.70(50)

when you solve, you should get b=20, c=30
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What I am wondering is, since this problem is a little different because it is with percentages, not money amounts, do I still have to do what Reiny told me for the one equation?

For example, here are my 2 equations

x + y = 20
Is the second equation:
.25x + .10y = .19
Or is it:
.25x + .10y = .19(20)

Thanks,
<3 Valeria <3

Answer 1

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Answer 2

You did not restate the second problem bu by the structure of your equations, I can tell it must be

.25x + .10y = .19(20) for the second equation.

Hint: multiply that equation by 100 to get rid of those nasty decimals, then from the first y=20-x
sub that back into the second and its easy from there on.
I got x=20

let me know if you did not get that.

Answer 3

Here's what I did

-10(.25x + .10y = .19(20))

I multiplied it by -10 so I could easily do the Elimination method.

That gets me:
-2.5x + -1y = -38

Then, I added the equations together to get:

-1.5x = -18

I divided both sides by -1.5 and that got me x = 12.

Did I go wrong somewhere? The thing is, then that makes y = 8, and when I substituted that into the second equation, it was correct. Were you wrong?

Thanks,
<3 Valeria <3

Answer 4

you are right,

when I looked back at my solution on the paper in front of me, I did have x =12
(I have no idea why I typed x = 20, perhaps I was looking at your previous question)

BTW, I had suggested multiplying by 100, since the longest decimal string has 2 places of decimal,
You multiplied by 10, which still left you with decimals to work with.
Of course if you are comfortable working with decimals, (a calculator doesn't care), then you could just as well work with the original equations

Answer 5

To solve the problem, you need to set up a system of equations based on the information given.

Let's assume x represents the weight (in pounds) of Deep Thought Granola and y represents the weight (in pounds) of Oat Dream Granola.

The first equation is the total weight equation, which states that the combined weight of Deep Thought and Oat Dream is 20 pounds:

x + y = 20

The second equation involves percentages. Deep Thought Granola is 25% nuts and dried fruit, while Oat Dream Granola is 10% nuts and dried fruit. You want the mixture to be 19% nuts and dried fruit.

To convert the percentages to decimals, you divide them by 100. So the second equation is:

0.25x + 0.10y = 0.19(20)

In this equation, the left side represents the total weight of nuts and dried fruit in the mixture, and the right side represents the desired weight of nuts and dried fruit in the 20-pound mixture.

Therefore, the correct equation is:

0.25x + 0.10y = 0.19(20)

Now you can solve the system of equations to determine the values of x and y.