Question

A recipe requires \[\dfrac{1}{3}\] cup of milk for each \[\dfrac{1}{4}\]cup of water. How many cups of water are needed for each cup of milk?

Answer 1

Hint: Problems like these are very easy to solve once we know and understand the underlying core concepts very well. This particular problem is a great example of unitary method and its application. Unitary methods in general have a wide variety of applications and are very useful while doing calculations which are linear in nature. This process is however not applicable in cases where the problem follows a definite function or equation. In this problem we first write the given statement, and then try to find the value for \[1\] cup, from this we can then find for any number of \[n\] cups of water.

Complete step by step solution:
Now we start off with the solution of the problem, by first of all writing down the given statement as,
\[\dfrac{1}{3}\] cup of milk \[\to \] \[\dfrac{1}{4}\]cup of water
Now, to find the number of cups of water for each cup of milk, we need to divide both the sides of the above equation by \[\dfrac{1}{3}\] , so the left hand side of the equation becomes \[1\] , which means for \[1\] cup of milk. Thus doing this, we get the answer as,
\[1\] cup of milk \[\to \] \[\dfrac{\dfrac{1}{4}}{\dfrac{1}{3}}\]cup of water
\[\Rightarrow 1\] cup of milk \[\to \] \[\dfrac{3}{4}\]cup of water
Thus, for each cup of milk we require \[\dfrac{3}{4}\] cups of water for the recipe.

Note: For such problems we need to have an in-depth knowledge of unitary method and its various applications. Using this method, we first of all need to find for \[1\] units and then we can easily find for \[n\] units by simply multiplying the result for one cup with \[n\] . We must also remember that this unitary method is applicable only for problems which are linear in nature and do not depend on any function or equation.