SOLUTION: A scientist wants to dilute 400 mL of a 16% saline solution to a 10% saline solution by adding water. How much water is needed? I am confused on how to set up the equation for

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Question 1152931: A scientist wants to dilute 400 mL of a 16% saline solution to a 10% saline solution by adding water. How much water is needed?
I am confused on how to set up the equation for the problem as i keep getting a negative number. The answer is 240 mL i just am unsure how to get there. Thank you!
Found 3 solutions by josgarithmetic, Boreal, ikleyn:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
400*0.16, represents amount of solute starting.

400+v, the amount of finished solution upon mixing in v mL.

---------------the addition of v mL. of water must bring saline concentration to 10%.

Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
x amount of water
400 ml * 0.16 saline=64 ml pure saline
add x water
(400+x)(0.10)=64 ml pure saline. Here, we know that if we add the right x of water, the whole solution will be 400+x ml, but the per cent will be 10
40+.10x=64
.10x=24
x=240 ml

Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website!
.

There is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - Unusual word problem on mixtures
    - Check if you know the basics of mixtures from Science
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a "bird flight height" (a top view) is the last lesson in the list.

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.