MHB Converting Salt Concentration to Algebraic Symbols

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To express the amount of salt in a tank holding x quarts of water with a concentration of 21 pounds per gallon, first convert the concentration to quarts, resulting in 21/4 pounds of salt per quart. This means that the total amount of salt, S, can be represented as S = (21/4)x. However, there is confusion regarding a book answer stating the amount is x/2 pounds, which may stem from a miscommunication about the concentration value. Clarification is needed on whether the original concentration was indeed 21 pounds or a different value, as 21 pounds per gallon is unusually high. The discussion highlights the importance of accurate unit representation in mathematical expressions.
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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!
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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