Question

Greta uses 3 ounces of pasta to make \[\dfrac{3}{4}\] of a serving pasta. How many ounces of pasta are there per serving?

Answer 1

Hint: From the question, it is given that Greta uses 3 ounces of pasta to make \[\dfrac{3}{4}\] of a serving pasta. So, for this question we use ratio and proportion concept and simplify using multiplication operation further to get our solution.


Complete step by step solution:
Let us assume that there are x number of ounces of pasta per serving.
We already know that we require 3 ounces of pasta to make \[\dfrac{3}{4}\] of a serving pasta.
So, we can write from ratio and proportion that,
\[\begin{align}
  & x\leftrightarrow 1 \\
 & 3\leftrightarrow \dfrac{3}{4} \\
\end{align}\]
Now by using cross multiplication, we get the equation reduced as follows.
\[\begin{align}
  & \Rightarrow x\left( \dfrac{3}{4} \right)=3(1) \\
 & \Rightarrow \dfrac{3x}{4}=3 \\
\end{align}\]
Now by using cross multiplication, we get the equation reduced as follows.
Here we will send the denominator in the left hand side of the equation to the right hand side of the equation. So, it will be multiplied to the numerator of the right hand side term of the equation.
\[\begin{align}
  & \Rightarrow 3x=3(4) \\
 & \Rightarrow 3x=12 \\
\end{align}\]
Now by using cross multiplication, we get the equation reduced as follows.
\[\begin{align}
  & \Rightarrow x=\dfrac{12}{3} \\
 & \Rightarrow x=4...(1) \\
\end{align}\]
So, from equation (1) it is clear that we require 4 ounces of pasta per serving.
Therefore, we got the solution as 4 ounces of pasta per serving.

Note: Students must be very careful in doing the calculations. We must have good knowledge in the concept of ratio and proportion. Students should not do mistake in cross multiplication for example in the step \[ x\left( \dfrac{3}{4} \right)=3(1)\] instead of this if write as \[ x\left( 3 \right)=\left( \dfrac{3}{4} \right)(1)\] our whole solution will be wrong.