Let's solve this step by step.
---
Step 1: Represent the sales data as matrices
We are given two types of staplers:
Standard and
Portable, each with three colors:
Black, Blue, Red. We have sales data for
last month and
this month.
We will create two matrices:
- One for
last month’s sales
- One for
this month’s sales
Each matrix will have rows for
Standard and
Portable, and columns for
Black, Blue, Red.
####
Matrix for Last Month:
$$
\text{Last Month} =
\begin{bmatrix}
124 & 143 & 108 \\
114 & 115 & 87
\end{bmatrix}
$$
- Row 1: Standard (Black, Blue, Red)
- Row 2: Portable (Black, Blue, Red)
####
Matrix for This Month:
$$
\text{This Month} =
\begin{bmatrix}
136 & 125 & 126 \\
98 & 123 & 101
\end{bmatrix}
$$
---
Step 2: Find the average sales over the 2-month period
To find the
average sales for each color and type, we add the two matrices and divide by 2.
$$
\text{Average} = \frac{1}{2} \left( \text{Last Month} + \text{This Month} \right)
$$
Add the matrices:
$$
\begin{bmatrix}
124 & 143 & 108 \\
114 & 115 & 87
\end{bmatrix}
+
\begin{bmatrix}
136 & 125 & 126 \\
98 & 123 & 101
\end{bmatrix}
=
\begin{bmatrix}
124+136 & 143+125 & 108+126 \\
114+98 & 115+123 & 87+101
\end{bmatrix}
=
\begin{bmatrix}
260 & 268 & 234 \\
212 & 238 & 188
\end{bmatrix}
$$
Now divide by 2:
$$
\text{Average} =
\begin{bmatrix}
130 & 134 & 117 \\
106 & 119 & 94
\end{bmatrix}
$$
---
Step 3: Fill in the Averages
From the average matrix:
-
Standard black: 130
-
Standard blue: 134
-
Standard red: 117
-
Portable black: 106
-
Portable blue: 119
-
Portable red: 94
---
✔ Final Answer:
Averages:
- Standard black:
130
- Standard blue:
134
- Standard red:
117
- Portable black:
106
- Portable blue:
119
- Portable red:
94
---
✔ Summary:
You correctly wrote the matrices for last month and this month. The final step was to compute the average by adding the two matrices and dividing by 2. The averages are now filled in above.
Parent Tip: Review the logic above to help your child master the concept of matrix word problems worksheet.
