Question

Your teacher asks you to find a recipe that includes two ingredients with a ratio of 1/2 cup/ 1/8 cup. a. give an example of two ingredients in a recipe that would meet this requirement. b. If you needed to triple the recipe, would the ratio change? Explain. C. What is the unit rate of the ingredients in your recipe? Please explain and work it out! Thank you!

Answer 1

case a) Give an example of two ingredients in a recipe that would meet this requirement

The example is with flour and sugar

Let

x--------> the number of cups of flour

y-------> the number of cups of sugar

we know that

$Ratio=\frac{x}{y}\\ \\x=\frac{1}{2} \ cup\ of\ flour\\\\ y=\frac{1}{8} \ cup\ of\ sugar \\ \\Ratio=\frac{(1/2)}{(1/8)}=4$

Part b) If you needed to triple the recipe, would the ratio change?

If the recipe is tripled, the ratio does not change, because both the amount of flour and the amount of sugar will also triple, leaving the ratio constant.

Example

$Ratio=\frac{x}{y}\\ \\x=3*\frac{1}{2} \ cup\ of\ flour\\\\ y=3*\frac{1}{8} \ cup\ of\ sugar \\ \\Ratio=\frac{(3/2)}{(3/8)}=4$

Part c) What is the unit rate of the ingredients in your recipe?

we know that

A unit rate is a rate in which the second rate is 1 unit

in this problem the unit rate is equal to $\frac{4}{1}\frac{cups\ of \ flour}{cup\ of\ sugar}$

That means the recipe requires $4$ cups of flour per cup of sugar

therefore

the answer Part c) is

The unit rate is equal to $\frac{4}{1}\frac{cups\ of \ flour}{cup\ of\ sugar}$