Question

Dakota paid $2.50 for 5 pounds of cherries for her infamous smoothie recipe. how much would Dakota pay, if she needed to double the recipe?(Write and solve by using a proportion).

Answer 1

So we must solve this by using a proportion. This means that we will have to solve an equation like this:

`(a)/(b)=(c)/(d)`

So, we know that the price per pund of cherries is constant. This is given by the total cost of a certain amount of pounds of cherries divided by the number of pounds. So the price per pound for her normal recipe is given by:

`\frac{\text{\$}2.50}{5\text{lbs}}`

If she needs to double the recipe then she must purchase 10 pounds. If we use x for how much she'll have to pay for these 10 pouns we get that the price per pound of cherries is:

`\frac{x}{10\text{lbs}}`

If we equalize both expressions for the price per pound of cherries we'll have the proportion equation like the one I stated before:

`\frac{\text{\$}2.50}{5\text{lbs}}=\frac{x}{10\text{lbs}}`

If we multiply both sides by 10lbs:

`\begin{gathered} \frac{\text{\$}2.50}{5\text{lbs}}\cdot10\text{lbs}=\frac{x}{10\text{lbs}}\cdot10\text{lbs} \\ x=2\cdot\text{\$}2.50=\text{\$}5 \end{gathered}`

Then the answer is x=$5.