SOLUTION: You have 30 cups of a drink that contains 75% juice concentrate. How many cups of a drink containing 68% juice concentrate needs to be added in order to have a final drink that is

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: You have 30 cups of a drink that contains 75% juice concentrate. How many cups of a drink containing 68% juice concentrate needs to be added in order to have a final drink that is       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1123653: You have 30 cups of a drink that contains 75% juice concentrate. How many cups of a drink containing 68% juice concentrate needs to be added in order to have a final drink that is 74% juice concentrate?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
0.75*30 + 0.68*x = 0.74*(30+x)


0.75*30 + 0.68x = 0.74*30 + 0.74x


0.75*30 - 0.74*30 = 0.74x - 0.68x


0.01*30 = 0.06x


x = %280.01%2A30%29%2F0.06 = 5.


Answer.  5 cups.

------------------

If you need more details or explanations, look into introductory lessons on mixture word problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.

Read them and become an expert in solution the mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
30 * .75 + x * .68 = (30 + x) * .74

that's your equation.

simplify to get 22.5 + .68 * x = .74 * 30 + .74 * x

simplify further to get 22.5 + .68 * x = 22.2 + .74 * x

subtract 22.2 from both sides of the equation and subtract .68 * x from both sides of the equation to get 22.5 - 22.2 = .74 * x - .68 * x

combine like terms to get .3 = .06 * x

solve for x to get x = .3 /.06 = 5

if you mix 30 cups of a 75% drink with 5 cups of a 68% drink, you will get 35 cups of a 74% drink.

30 * .75 + 5 * .68 = 25.9

35 * .74 = 25.9

30 * .75 + 5 * .68 = 35 * .74

solution is confirmed to be good.

solution is 5 cups of 68% juice concentrate are added to 30 cups of 75% juice concentrate to get 35 cups of 74% juice concentrate