Mixture to create a 50% acid solution?

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Discussion Overview

The discussion revolves around a mathematical problem involving the mixing of acid solutions to achieve a desired concentration. Participants explore the setup of an equation to determine how much of a 10% acid solution is needed to mix with a given volume of an 80% acid solution to create a 50% acid solution.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents an equation to determine the volume of a 10% acid solution needed, stating: "0.10x + 55(0.80) = 0.50(x + 55)" and questions if this setup is correct.
  • Several participants confirm that the equation correctly represents the amount of acid on both sides.
  • Another participant states they solved for x and obtained a value of 41.25 milliliters, asking if this result is correct.
  • There is a concern raised about the decimal nature of the answer (41.25 mL) in contrast to the whole number (55 mL) provided in the problem, questioning the sensibility of the result.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical setup of the problem and the correctness of the equation. However, there is uncertainty regarding the interpretation of the decimal result in the context of the problem.

Contextual Notes

The discussion does not resolve the implications of obtaining a decimal value in the context of the problem, nor does it address any assumptions regarding the mixing process or the definitions of concentration used.

mathdad
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How many milliliters of a 10% acid solution must be added to 55 milliliters of a 80% acid solution to create a 50% acid solution?

This is my equation set up:

0.10x + 55(0.80) = 0.50(x + 55)

Is this correct?
 
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Yes, you have the amount of acid (in mL) on both sides of the equation. (Yes)
 
MarkFL said:
Yes, you have the amount of acid (in mL) on both sides of the equation. (Yes)

All I have to do is solve for x, right?

- - - Updated - - -

I got x = 41.25.Is this right?
 
RTCNTC said:
All I have to do is solve for x, right?

- - - Updated - - -

I got x = 41.25.Is this right?

Mathematically, yes.
 
Joppy said:
Mathematically, yes.

Ok. So, the answer is 41.25 milliliters of a 10% acid solution. Does this even make sense? Why is this answer for milliliters a decimal number while the given milliliter is 55, a whole number? See my point?
 

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