Question

A 6 ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10 ounce package?

Answer 1

Hint: We will use the unitary method to solve this question. We will see the definition of unitary method. We will find the number of pieces in a 1 ounce package of fruit snacks. For this, we will use the information given for the 6 ounce package. Then we will multiply this quantity by 10 to obtain the number of pieces in a 10 ounce package.

Complete step by step answer:
The unitary method is a method of problem solving in which we use the given value of a multiple to find the value of a single unit. Then we use this value of the single unit and calculate the required value of the other multiple.
We are given that there are 45 pieces in a 6 ounce package of fruit snacks. So, we can find the number of pieces in a 1 ounce package by dividing 45 by the number 6.
$\begin{align}
  & 6\text{ ounce package}:45\text{ pieces} \\
 & \text{1 ounce package}:x\text{ pieces} \\
\end{align}$
Therefore, by cross multiplying the above ratios, we have the following,
$\begin{align}
  & x=\dfrac{45}{6} \\
 & \therefore x=7.5 \\
\end{align}$
Now, we have to find the number of pieces in a 10 ounce package. So, we will multiply the value of a single unit by 10 to obtain the number of pieces in a 10 ounce package.
$\begin{align}
  & \text{1 ounce package}:7.5\text{ pieces} \\
 & \text{10 ounce package}:y\text{ pieces} \\
\end{align}$
Therefore, cross multiplying the above ratios, we get that
$\begin{align}
  & y=7.5\times 10 \\
 & \therefore y=75 \\
\end{align}$

Hence, there are 75 pieces in a 10 ounce package of fruit snacks.

Note: It is important to write the ratios correctly, so that we can avoid any confusion in the given information. The unitary method is a very important technique to solve such problems. Mostly, we have to use this method while solving word problems. We should interpret the word problem statements correctly and then determine the method needed to solve them.