Question

Anjali used $\dfrac{1}{3}$ of the butter in making sauce. She used $\dfrac{5}{8}$ of the remaining to make garlic bread. What fraction of the butter did she have used in making garlic bread?

Answer 1

Hint: We shall assume that the total butter Anjali had as ‘$x$’. The amount of butter she used in making sauce is $\dfrac{1}{3}$ . She still had $x-\dfrac{1}{3}x$ butter left with her after preparing the sauce. Then, she used $\dfrac{5}{8}$ of the remaining butter in making garlic bread. The amount of butter she used in making garlic bread $\left( x-\dfrac{1}{3}x \right) \times \dfrac{5}{8}$. The amount of butter she used for garlic bread out of total amount of butter is :- $\dfrac{\left( x-\dfrac{1}{3}x \right) \times \dfrac{5}{8}}{x}$.

Complete step-by-step answer:
Let us now solve this question.
We had assumed the total butter used by Anjali to be ‘$x$’. We are given the question that she used $\dfrac{1}{3}$ of the total butter in making sauce. So the amount of butter she used to make the sauce in $x$ is $\dfrac{1}{3}x.$
The amount of butter remaining with her is the difference of total butter $x$ and the butter used up in making the sauce $\dfrac{1}{3}x.$ . So the amount of butter remained after the making of sauce is
\[x-\dfrac{1}{3}x=x\left( 1-\dfrac{1}{3} \right)=x\left( \dfrac{3-1}{3} \right)=\dfrac{2}{3}x\]
We are also given the question that she used $\dfrac{5}{8}$ of the remaining to make garlic bread. So the amount of butter she used to make garlic bread in $x$ is $\dfrac{5}{8}$ of $\dfrac{2}{3}x$ which is
\[\dfrac{5}{8}\times \dfrac{2}{3}x=\dfrac{5}{12}x\]
The part of total butter she used to make garlic bread is the ratio of the used up butter to make garlic bread $\dfrac{5}{12}$ to the total butter $x$ which is

\[\left( \dfrac{5}{12}x \right)\div x=\dfrac{5}{12}\]

So, the answer of this question is $\dfrac{5}{12}$

Note: The keyword is here ‘remaining ‘.If we ignore’ remaining’ unknowingly the amount of butter for the garlic bread will be $\dfrac{5}{8}x$ which is incorrect as per the question. We note that we can only divide $x$ because $x$ cannot be zero. If the total amount $X$ of any substance is divided in a ratio $a:b$ then we can express the total as $X=ax+bx$ where $x$ is the unknown.