Trey Montes

2023-03-28

Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound? ### Answer & Explanation nickalasaurus6ea0 Beginner2023-03-29Added 5 answers$/pound will be used as the "units". Calculations will involve converting ounces to pounds. The value of our conversion ratio is:
16 ounce/pound
To ensure that the mathematical value you will calculate corresponds to the desired real answer, use "Dimensional Analysis."
$\frac{2.40}{3oz}\cdot \frac{16oz}{pound}=\frac{12.80}{pound}$
Remember – the MATH will always give you some number! For it to be correct and useful, you need to make sure that the dimensions describe what you want.

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The model's development
Transform the given data into ratio form, but in fractional form.
When you see the wording: $\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\prime \underline{\text{per}}$ pound' you are being told "for each pound" and this is to be the denominator (bottom number) of the ratio (fraction).
So we have:$\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\frac{\text{cost}}{\text{1 pound}}$ as our target
Note that 1 pound is 16oz
$\frac{2.40}{3oz}\equiv \frac{\text{cost}}{16oz}=\frac{\text{cost}}{\text{1 pound}}$
The sign $\equiv$ means equivalent to
Let x be the unknowable cost, thus:
$\frac{2.40}{3oz}\equiv \frac{x}{16oz}=\frac{x}{\text{1 pound}}$
Therefore, if we can figure out a way to convert the 3 oz to 16 oz and then do the same for the numerator (top number), then we have the solution.

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