Question

A bag of chips is 24 ounces. A serving size is $\dfrac{3}{4}$ of an ounce. How many servings are in the bag of chips? \[\]

Answer 1

Hint: We recall what ounce and serving size means. We see that the more number of servings more than the sum of weights of servings. So we find the number of servings by dividing the weight of the bag of the chips by the weight of one serving. \[\]

Complete step-by-step solution:
We know that ounce is measure of weight which is ${{\left( \dfrac{1}{16} \right)}^{\text{th}}}$ of pound and a serving size is the standard unit with recommended amount of nutrition. We are given in the question the weight of a bag of chips that is 24 ounces. We are also given the question of the weight of serving size as $\dfrac{3}{4}$ of an ounce. So the number of servings is the total weight of the servings by weight of one serving. Since the total weight of the servings size is equal to the weight of bag of chips, we have
\[\begin{align}
  & \text{Number of servings }=\dfrac{\text{Weight of the bag of chips}}{\text{Weight of one serving }} \\
 & \Rightarrow \text{Number of servings }=\dfrac{24}{\dfrac{3}{4}} \\
\end{align}\]
We know how to divide fractions. We multiply the numerator fraction with the reciprocal denominator fraction. Here the denominator fraction is $\dfrac{3}{4}$ whose reciprocal is $\dfrac{4}{3}$. So we have
\[\begin{align}
  & \Rightarrow \text{Number of servings }=24\times \dfrac{4}{3} \\
 & \Rightarrow \text{Number of servings }=\dfrac{96}{3}=32 \\
\end{align}\]
So there are 32 servings in the bag.

Note: We can alternatively solve using linear equations. Let us assume the number of servings is $x$. Since we are given the weight of one serving is $\dfrac{3}{4}$ the total weights of the servings are $\dfrac{3}{4}x$ which is equal to the weight of the bag of chips given to us as 24 ounce. So we have
\[\begin{align}
  & \dfrac{3}{4}x=24 \\
 & \Rightarrow \dfrac{3x}{4}=\dfrac{24}{1} \\
\end{align}\]
We cross multiply to have;
\[\begin{align}
  & \Rightarrow 3x\times 1=24\times 4 \\
 & \Rightarrow 3x=96 \\
\end{align}\]
We divide both sides by 3 to have;
\[\Rightarrow x=\dfrac{96}{3}=32\]
So there are 32 servings in the bag.