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?

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.

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.

shorteghurlxh0m

Beginner2023-03-30Added 10 answers

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.

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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?

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