Converting Salt Concentration to Algebraic Symbols

[paulmdrdo1]

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!

 

[Deveno]

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...?

 

[paulmdrdo1]

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

but the answer in my book is $\frac{x}{2}$lb salt. why is that?

 

[Deveno]

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"...

 

[HallsofIvy]

I don't think it is possible to dissolve 21 pounds of salt in a gallon!