Converting Salt Concentration to Algebraic Symbols

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Discussion Overview

The discussion revolves around expressing the amount of salt in a tank of water in algebraic symbols, specifically focusing on converting a concentration given in pounds per gallon to a formula involving quarts of water. The scope includes mathematical reasoning and clarification of units.

Discussion Character

  • Mathematical reasoning, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests using the variable $S$ to represent the salt concentration per quart, calculating it as $\frac{21}{4}$ pounds per quart based on the given concentration of 21 pounds per gallon.
  • Another participant proposes that the total amount of salt can be expressed as $\frac{21}{4}x$, where $x$ is the number of quarts.
  • A different participant questions this calculation, noting a discrepancy with a book answer of $\frac{x}{2}$ pounds of salt and seeks clarification on the reasoning behind the difference.
  • One participant raises a concern about the feasibility of dissolving 21 pounds of salt in a gallon of water, suggesting a potential misunderstanding in the problem statement.

Areas of Agreement / Disagreement

Participants express differing views on the correct conversion and representation of salt concentration, with no consensus reached regarding the correct algebraic expression or the feasibility of the salt amount.

Contextual Notes

There is ambiguity regarding the initial concentration of salt, as well as potential confusion in unit conversions and the physical plausibility of the quantities involved.

paulmdrdo1
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express in algebraic symbols

The amount of salt in a tank holding x quarts of water if the concentration is 21lb of salt per gallon.

please help! thanks!
 
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One of the things we do is let letters stand for the quantities we wish to represent. In this case, $S$ is a natural letter to use for: "salt per one quart".

Now we are actually GIVEN: "salt (in pounds) per gallon". So the first thing to do is convert gallons to quarts.

As there are 4 quarts to a gallon, this means the ratio of salt (in pounds) to quarts is:

$\dfrac{21 \text{ pounds}}{4 \text{ quarts}}$,

that is: $\dfrac{21}{4}$ pounds per quart. So:

$S = \dfrac{21}{4}$.

Now, if we multiply that by $x$ quarts, we get...?
 


$\frac{21}{4}x$?

but the answer in my book is $\frac{x}{2}$lb salt. why is that?
 
Perhaps you typed 21lbs, when you actually meant: 2lbs? It helps to put a space between your number, and the units, since a lower case "L" looks a lot like a "1"...
 
I don't think it is possible to dissolve 21 pounds of salt in a gallon!
 

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