Question

You need 1 1/4 cups of sugar to make 20 cookies To make 6 cookies, you will need cups of sugar. Enter your answer as a fraction or whole number.

Answer 1

We know that we need 1 1/4 cups of sugar to make 20 cookies, and we would like to know how many cups of sugar are needed to make 6 cookies. For doing so, we will use the rule of three.

In this case, we have two magnitudes: cups of sugar and cookies. Also we know that if we need to make more cookies, we need more cups of sugar, and so, the magnitudes are directly proportional. So, we will use a direct rule of three.

Also, we know that:

`1(1)/(4)=(5)/(4)`

And we can do our rule of three, assuming x represents the value of the cups of sugar needed to make 6 cookies.

`((5)/(4))/(20)=(x)/(6)`

We will do the product of means and the product of extremes. And we obtain:

`\begin{gathered} (5)/(4)\cdot6=20\cdot x \\ (30)/(4)=20\cdot x \\ (15)/(2)=20\cdot x \end{gathered}`

Lastly, we divide both sides by 20, to get:

`\begin{gathered} ((15)/(2))/(20)=x \\ (15)/(40)=x \end{gathered}`

And simplifying, we obtain that:

`x=(3)/(8)`

This means that we need 3/8 cups of sugar to make 6 cookies.