Exploring Matrix Applications: Word Problems for Grade 9

A store sells 3 types of fruits: apples, bananas, and cherries. The sales for each type of fruit in three different weeks are represented by the matrix \( A = \begin{bmatrix} 30 & 20 & 10 \\ 25 & 15 & 5 \\ 40 & 30 & 20 \end{bmatrix} \). If the store wants to find the total sales for each type of fruit over the three weeks, what is the resulting matrix?

• [95, 65, 35]

• [90, 60, 20]

• [80, 50, 30]

• [100, 70, 40]

A company produces two products, A and B. The profit from each product is represented by the matrix \( P = \begin{bmatrix} 50 & 70 \end{bmatrix} \) and the number of products sold each month is given by the matrix \( Q = \begin{bmatrix} 100 \\ 150 \end{bmatrix} \). Calculate the total profit for the month using matrix multiplication.

• 15500

• 16000

• 14000

• 15000

A school has 4 classes with different numbers of students. The number of students in each class is represented by the matrix \( S = \begin{bmatrix} 25 & 30 & 20 & 15 \end{bmatrix} \). If each student needs 3 notebooks, how many notebooks does the school need in total?

• 240

• 180

• 300

• 270

A transportation company uses a matrix to represent the number of vehicles of different types: cars, trucks, and buses. The matrix is \( V = \begin{bmatrix} 10 & 5 & 2 \end{bmatrix} \). If each car can carry 4 passengers, each truck can carry 10, and each bus can carry 30, how many passengers can be transported in total?

• 120

• 200

• 150

• 180

A restaurant has a menu with three items: burgers, pizzas, and salads. The sales for each item over a week are represented by the matrix \( M = \begin{bmatrix} 50 & 40 & 30 \\ 60 & 50 & 40 \\ 70 & 60 & 50 \end{bmatrix} \). What is the total sales for each item over the week?

• {"burgers": 180, "pizzas": 150, "salads": 120}

• burgers: 160, pizzas: 140, salads: 130

• burgers: 150, pizzas: 180, salads: 100

• burgers: 200, pizzas: 120, salads: 90

A graphic designer uses a transformation matrix to scale an image. The original coordinates of a triangle are represented by the matrix \( T = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} \). If the scaling factor is 2, what are the new coordinates of the triangle after the transformation?

• [[1, 2], [3, 4], [5, 6]]

• [[0, 0], [0, 0], [0, 0]]

• [[2, 4], [6, 8], [10, 12]]

• [[4, 8], [12, 16], [20, 24]]

A farmer has a field divided into three sections. The area of each section is represented by the matrix \( F = \begin{bmatrix} 10 & 15 & 20 \end{bmatrix} \) acres. If the farmer wants to plant 5 trees per acre, how many trees will he plant in total?

• 225 trees

• 300 trees

• 150 trees

• 180 trees

A delivery service has three routes with different delivery times represented by the matrix \( D = \begin{bmatrix} 30 & 45 & 60 \end{bmatrix} \) minutes. If the service wants to find the total delivery time for 4 deliveries on each route, what is the resulting matrix?

• [120, 180, 240]

• [150, 225, 300]

• [90, 135, 180]

• [100, 150, 200]

A video game company tracks the number of copies sold for three games over four months. The sales data is represented by the matrix \( G = \begin{bmatrix} 100 & 150 & 200 \\ 120 & 180 & 240 \\ 130 & 190 & 260 \\ 140 & 200 & 280 \end{bmatrix} \). What is the total number of copies sold for each game over the four months?

• [480, 710, 950]

• [400, 600, 800]

• [490, 720, 980]

• [500, 700, 900]

A city is planning to build parks in three neighborhoods. The budget for each neighborhood is represented by the matrix \( B = \begin{bmatrix} 50000 & 75000 & 100000 \end{bmatrix} \). If the city allocates 20% of the budget to each neighborhood, how much money will be allocated to each park?

• [10000, 15000, 20000]

• [20000, 30000, 40000]

• [12000, 18000, 24000]

• [8000, 12000, 16000]