SOLUTION: Your 10 gallons of 40% grape juice is too sweet. How many gallons of 10% grape juice should be added to make 30% grape juice?

Question 1135500: Your 10 gallons of 40% grape juice is too sweet. How many gallons of 10% grape juice should be added to make 30% grape juice?
Found 4 solutions by ikleyn, josgarithmetic, MathTherapy, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

0.40*10 + 0.1*x = 0.3*(10+x) 4 + 0.1x = 3 + 0.3x 4 - 3 = 0.3x - 0.1x x = = 5. ANSWER. 5 liters of the 10% juice to add.

Solved.

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It is a standard and typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.

Read them and become an expert in solution 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 textbook in the section "Word problems" 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 josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

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check

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Your 10 gallons of 40% grape juice is too sweet. How many gallons of 10% grape juice should be added to make 30% grape juice?

Let amount of 10% juice to be added, be T
Then we get: .1T + .4(10) = .3(T + 10)
.1T + 4 = .3T + 3
.1T - .3T = 3 - 4
- .2T = - 1
Amount of 10% juice to add, or
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

So far, you have received 3 responses showing similar yet different algebraic methods for solving the problem.

Here is an alternative which, if you understand how to use it, gets you to the answer to a mixture problem like this much faster and with far less effort.

You are starting with 40% grape juice and adding 10% grape juice; you want to stop when the mixture is 30% grape juice.

30% is 1/3 of the way from 40% to 10%; that means 1/3 of the mixture must be what you are adding.

So 1/3 of the mixture is the 10% grape juice you are adding; so 2/3 of the mixture is the 40% grape juice you started with. That means the 10% and 40% juices need to be mixed in the ratio 1:2.

Then since you used 10 gallons of the 40% juice, you need 5 gallons of the 10% juice.
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