Question

Two ounces of a breakfast shake provide $6$ grams of protein. How many ounces of the product would be needed to provide $72$ grams of protein?

Answer 1

Hint: In the problem we need to calculate the number of ounces required to provide $72$ grams of protein while $2$ ounces provide $6$ grams. For this we will first calculate how many proteins we will get for one ounces from the statement ‘ $2$ ounces provide $6$ grams of protein’. Now we will assume the number of ounces required as $x$ and we will calculate how many grams of protein we will get for this $x$ number of ounces. Now we will equate this value to the $72$ and simplify the equation to get the required solution.

Complete step-by-step solution:
Given that, $2$ ounces provide $6$ grams of protein.
From the above statement we can calculate the grams of protein we will get for one ounce as
$\begin{align}
  & \Rightarrow p=\dfrac{6}{2} \\
 & \Rightarrow p=3 \\
\end{align}$
That means we will get $3$ grams of protein for one ounce.
Let us assume the number of ounces as $x$. For $x$ ounces the amount of protein we will get is given by
$\begin{align}
  & \Rightarrow {{p}_{x}}=x\times p \\
 & \Rightarrow {{p}_{x}}=x\times 3 \\
 & \Rightarrow {{p}_{x}}=3x \\
\end{align}$
If we want to get $72$ grams of protein for $x$ ounces, then
$\begin{align}
  & \Rightarrow {{p}_{x}}=72 \\
 & \Rightarrow 3x=72 \\
\end{align}$
Dividing the above equation with $3$ on both sides, then we will get
$\begin{align}
  & \Rightarrow \dfrac{3x}{3}=\dfrac{72}{3} \\
 & \Rightarrow x=24 \\
\end{align}$
Hence we need a $24$ number of ounces to get $72$ grams of the protein.

Note: We can also solve this problem in another method. We reframe the question as for $6$ grams of protein we need $2$ ounces and for $72$ grams of protein how many ounces we need. From this statement we can write the equation
$\begin{align}
  & \Rightarrow \dfrac{6}{2}=\dfrac{72}{x} \\
 & \Rightarrow 3=\dfrac{72}{x} \\
 & \Rightarrow x=\dfrac{72}{3} \\
 & \Rightarrow x=24 \\
\end{align}$
From both the methods we got the same result.