SOLUTION: Mrs. Ernsthausen wants to create a sugar solution for her hummingbird feeder. She has a 20% sugar solution. She has learned that a 25% sugar solution is optimal. How many cups of p

Algebra.Com
Question 1114594: Mrs. Ernsthausen wants to create a sugar solution for her hummingbird feeder. She has a 20% sugar solution. She has learned that a 25% sugar solution is optimal. How many cups of pure sugar and 20% sugar solution does she need to mix together to make two cups of 25% sugar solution?
Found 2 solutions by VFBundy, ikleyn:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
x = 20% sugar solution
y = 100% (pure) sugar solution

Make two equations. The first equation is the total amount of solution. The second equation is the total amount of sugar in the solution.
x + y = 2
0.20x + y = 0.25(2)

Clean up the second equation:
x + y = 2
0.20x + y = 0.50

Multiply the second equation by -1:
x + y = 2
-0.20x - y = -0.50

Add the two equations together:
0.80x = 1.50

Solve for x:
x = 1.875

We now know the 20% solution (x) is 1.875 cups. Because x + y = 2...or, 1.875 + y = 2...that means the pure sugar solution (y) is 0.125 cups.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            This problem is posed incorrectly (or at least incompletely) in this post.

            Here I want to explain why it is incorrect (or at least incomplete). 


First, the concentration of solutions in this problem is in grams per liter.
Grams of sugar per liter of water.


It is not in cups of sugar per cup of water.


Also, the person who solves this problem, must know that the volumes are not added when a cup of sugar is dissolved in water.


These are elementary knowledge from Science that the student must possess when he starts solving the problems like this one.


So, to have the formulation complete, the density of the sugar in the cup must be given,
and the primary unknown should be the mass of sugar, but not the number of cups of sugar.


Warning :  when you start solving a problem on mixtures and concentrations, the first thing you must clearly understand is


    in which units the concentration is measured / (is given) ?


It can be [volume-to-volume], [mass-to-mass] or [mass-to-volume].


All these things are clearly explained in my lessons

    - Mixture problems

    - More Mixture problems

in this site.


Again, these knowledge is the minimum student must possess about physics of solutions to solve such problems consciously.


There is no need to explain that the person who positions himself as a "problems-creator" or a "tutor" must know it perfectly.


This my post is addressed to the person who posted/created this problem, as well as to the tutor @VFBundy.

Have a nice day !


RELATED QUESTIONS

Julia wants to make 20 fl. oz. of a 65% sugar solution by mixing together a 85% sugar... (answered by jorel1380)
Jan wants to make 15L of a 14% sugar solution by mixing together a 20% sugar solution and (answered by ikleyn)
Mrs. Martinez mixes a 90% sugar cinnamon flavored solution with a 95% sugar... (answered by josgarithmetic)
Anjali wants to make 10.5 qt. of 50% sugar solution by mixing together a 70% sugar... (answered by mananth)
I’m not sure how to set up this problem: Jimmy wants to make a 48% sugar solution. (answered by Alan3354)
Ted wants to make a 48% sugar solution. He has already poured 7 fl. oz of a 32% sugar... (answered by lwsshak3)
is it possible to mix a 20% sugar solution with a 40% sugar solution to get a 60% sugar... (answered by oberobic)
Is it possible to mix a 10% sugar solution with a 20% sugar solution to get a 30% sugar... (answered by Edwin McCravy)
Franz intends to mix a solution containing 11% sugar with 24 miligrams of a solution... (answered by ankor@dixie-net.com)