Question

A cookie recipe called for 2 4/5 cups of sugar for every 2/3 cup of flour. If you made a batch of cookies using 1 cup of flour, how many cups sugar would you needs

Answer 1

`4(1)/(5) cups`

Explanation:

Let's start by setting up a ratio for the recipe.

First, rewrite 2 and 4/5 as an improper fraction.

`2(4)/(5) = (14)/(5)`

We know that for every 2/3 cup of flour, we need 14/5 cups of sugar. So, our ratio will be:

`(2)/(3) :(14)/(5)`

We want to find how many cups of sugar we'd need for 1 cup of flour. Let s represent the cups of sugar. Let's set up another ratio (flour to sugar):

`1:s`

Now, since you're following the same recipe, let's set the ratios equal to make a proportion, like so:

`(2)/(3) :(14)/(5) =1:s`

Multiply the means and extremes, set their products equal, and solve.

`(2)/(3)s=(14)/(5)*1=\\s=(3)/(2) *(14)/(5) =\\s=(21)/(5)`

Let's turn 21/5 into a mixed number.

`(21)/(5) =4(1)/(5)`

So, if you used one cup of flour, you would need
`4(1)/(5)` cups of sugar.