Question

A chocolate chip cookie recipe ask for 3 3/4 times as much flour as chocolate chips. If 2 1/2 cups of flour is used what quantity of chocolate chips would then be needed

Answer 1

If the recipe asks for 3 3/4 times as much flour as chocolate chips, it means taht for each 1 chocolate chips, we will need 3 3/4 flour.

So, let's first convert the number fraction to a single fraction.

3 3/4 means 3 units plus 3/4, so:

`3+(3)/(4)=3\cdot(4)/(4)+(3)/(4)=(12)/(4)+(3)/(4)=(15)/(4)`

Let's also convert the new quantity of flour into a single fraction.

2 1/2 is:

`2+(1)/(2)=2\cdot(2)/(2)+(1)/(2)=(4)/(2)+(1)/(2)=(5)/(2)`

Since we need to proportionally adjust the quantity of chocolate chips, the ratio between the recipe quantity and the new quantity has to be the same for the flour and the chocolate chips.

The ratio for the flour is:

`((5)/(2))/((15)/(4))=(5)/(2)\cdot(4)/(15)=(2)/(3)`

Let "x" be the new quantity of chocolate chip. Its ratio is:

`(x)/(1)`

And this ratio must be the same as the flour's, so:

`\begin{gathered} (x)/(1)=(2)/(3) \\ x=(2)/(3) \end{gathered}`

Thus, the quantity of chocolate chips needed is 2/3.