Word Problems: Mixture

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bebe123abc

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May 31, 2007
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I don't know how to set this up:

How many gallons of a 70% salt solution must be mixed with 80 gallons of a 22% solution to obtain a solution that is 60% salt? :?
 
let x = number of gallons of 70% solution

(x gallons)(70% salt) + (80 gallons)(22% salt) = (x + 80 gallons)(60% salt)

solve for x
 
Hello, bebe123abc!

Here's my baby-talk approach . . .

How many gallons of a 70% salt solution must be mixed with 80 gallons of a 22% solution
to obtain a solution that is 60% salt?
Click to expand...

We have 80 gallons which is 22% salt.
. . It contains: \(\displaystyle \,0.22\,\times\,80 \:=\:17.6\) gallons of salt.

We add \(\displaystyle x\) gallons which is 70% salt.
. . It contains: \(\displaystyle \,0.70x\) gallons of salt.

So the final mixture will contain: \(\displaystyle \,\fbox{17.6\,+\,0.70x}\) gallons of salt. .[1]


Look at it another way.

We had 80 gallons of solution and we added \(\displaystyle x\) gallons of another solution.
. . The mixture contains \(\displaystyle x\,+\,80\) gallons of stuff.
Since this is suppose to be 60% salt,
. . the final mixture will contain: \(\displaystyle \,\fbox{0.60(x\,+\,80)}\) gallons of salt. .[2]


We have expressed the final amount of salt in two ways.
. . Hence, [1] and [2] are equal.

There is our equation! . \(\displaystyle 17.6\,+\,0.70x \;=\;0.60(x\,+\,80)\)

 
Thanks a lot. Can you help me set up the equation for both of these too
?

A juice drink manufaturer has found mixing pineapple juice concentrate and fresh squeezed orange juice is the most cost effective way to produce its breakfast beverage. The pineapple juice comes in two concentrated forms, 18% and 30% pineapple juice, which must be combined into a solution that can be mixed with the orange juice. If 20 gallons of 18% juice is used, how many gallons of the 30% juice must be used to obtain a 20% pineapple juice solution?

The other one is:
How many pounds of gourmet candy selling for $1.20 per pound should be mixed with 5 pounds of gourmet candy selling for $2.40 per pound to obtain a mixture selling for $1.80 per pound?
 
The idea is for you to understand the principles. Setting up the problem is the part that you should be learning. You studied all the algebra and arithmetic in some earlier course or unit.

So, what are your thoughts? How would you set them up using the principles discussed above?
 
Thank you, but could you please explain how to set up this equation because this is a different problem than the one posted above?
 
Soroban took his time to go above and beyond in a detailed and thorough explanation in regards to your original post.

Honestly, how much more explaining is needed?

John.
 
bebe123abc said:
I know but as I mentioned before this is a different problem.
Click to expand...
Different problem, same idea!
You just want someone to do it for you. Don't you?
 
You were given a WONDERFUL explanation that should apply to ANY mixture problem.

Yes....the specifics of the two other problems you posted are "different." But, they are both mixture problems and the method described by Soroban will apply to both of them.

Please try them on your own. If you can't "get" an answer which checks, then please repost, showing ALL of the steps you tried (even if you think they're wrong.)

We can only see where your difficulties lie when you show us what you tried. Just expecting us to give an answer won't help you learn to solve problems on your own.
 
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