Question

Emma is making a cookie recipe that requires 4 cups of sugar for every 8 cups of flour. Emma only has 6 cups of flour. She concludes that she will only need 3 cups of sugar. Is Emma correct? Why or why not?

Answer 1

She will only need 3 cups of sugar, so Emma is correct.

Explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed, where a, b and c are known values ​​and x an unknown value

a ⇒ b

c ⇒ x

Then:
`x=(c*b)/(a)`

In this case, the following rule of three can be applied: if for every 8 cups of flour 4 cups of sugar are required, for every 6 cups of flour how many cups of sugar are required?

`cups of sugar=(6 cups of flour*4 cups of sugar)/(8 cups of flour)`

cups of sugar=3

She will only need 3 cups of sugar, so Emma is correct.