Grade 9 Matrix Equations: Real-World Word Problems

A company produces two types of gadgets, A and B. The profit from each gadget A is $5 and from gadget B is $8. If the company produces a total of 100 gadgets and the profit from all gadgets is $600, set up a matrix equation to find how many of each type were produced.

• x + y = 100; 5x + 8y = 600.

• x + y = 50; 5x + 8y = 300.

• x + y = 100; 5x + 8y = 500.

• x + y = 200; 5x + 8y = 800.

In a school, the ratio of boys to girls is 3:2. If there are 120 students in total, represent this situation using a matrix and solve for the number of boys and girls.

• Boys: 72, Girls: 48

• Boys: 50, Girls: 70

• Boys: 60, Girls: 60

• Boys: 80, Girls: 40

A store sells two types of shoes: sneakers and boots. The total number of shoes sold is 150, and the revenue from sneakers is $30 per pair while boots are $50 per pair. If the total revenue is $5000, create a matrix equation to find the number of each type sold.

• x + y = 200, 30x + 60y = 6000

• x + y = 150, 25x + 45y = 4500

• x + y = 150, 30x + 50y = 5000

• x + y = 100, 20x + 40y = 4000

A farmer has a total of 200 acres of land divided into corn and wheat. If the corn yields $300 per acre and wheat yields $200 per acre, and the total income from both crops is $50,000, set up a matrix to solve for the acres of each crop.

• x = 100 acres of corn and y = 100 acres of wheat.

• x = 200 acres of corn and y = 0 acres of wheat.

• x = 80 acres of corn and y = 120 acres of wheat.

• x = 150 acres of corn and y = 50 acres of wheat.

A delivery service has two types of packages: small and large. The small package costs $10 to deliver and the large package costs $15. If the total number of packages delivered is 200 and the total delivery cost is $2500, create a matrix equation to find the number of each type of package delivered.

• x = 200, y = 0

• x = 100, y = 100

• x = 150, y = 50

• x = 50, y = 150

In a concert, the ratio of tickets sold for adults to children is 4:1. If the total revenue from ticket sales is $8000, with adult tickets priced at $50 and children's tickets at $20, set up a matrix to find the number of adult and child tickets sold.

• 120 adult tickets and 40 child tickets

• 100 adult tickets and 50 child tickets

• 145 adult tickets and 36 child tickets

• 160 adult tickets and 20 child tickets

A restaurant offers two types of meals: vegetarian and non-vegetarian. If the total number of meals served is 180 and the revenue from vegetarian meals is $12 each while non-vegetarian meals are $18 each, create a matrix equation to determine how many of each type of meal was served.

• The matrix equation is: [[1, 1], [12, 18]] * [[x], [y]] = [[180], [R]].

• [[1, 1], [10, 20]] * [[x], [y]] = [[180], [R]].

• [[0, 1], [0, 18]] * [[x], [y]] = [[180], [R]].

• [[1, 0], [12, 0]] * [[x], [y]] = [[180], [R]].

A school is organizing a field trip and has two types of buses: small and large. The small bus can carry 20 students and the large bus can carry 50 students. If the total number of students going is 200, set up a matrix to find how many of each type of bus is needed.

• 5 small buses and 1 large bus.

• 0 small buses and 4 large buses.

• 4 small buses and 0 large buses.

• 2 small buses and 4 large buses.

A factory produces two products, X and Y. The production of X requires 3 hours of labor and Y requires 2 hours. If the factory has 120 hours available and produces a total of 40 products, create a matrix equation to find how many of each product is produced.

• Product X: 10, Product Y: 30

• Product X: 30, Product Y: 10

• Product X: 20, Product Y: 20

• Product X: 25, Product Y: 15

A clothing store sells shirts and pants. The store has a total of 300 items, and the revenue from shirts is $25 each while pants are $40 each. If the total revenue is $8000, set up a matrix equation to find the number of shirts and pants sold.

• The matrix equation is \[ \begin{bmatrix} 1 & 2 \\ 30 & 50 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 300 \ \ 7000 \end{bmatrix} \].

• The matrix equation is \[ \begin{bmatrix} 1 & 1 \\ 25 & 40 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 300 \\ 8000 \end{bmatrix} \].

• The matrix equation is \[ \begin{bmatrix} 2 & 1 \\ 25 & 40 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 300 \ \ 9000 \end{bmatrix} \].

• The matrix equation is \[ \begin{bmatrix} 1 & 1 \\ 20 & 30 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 300 \ \ 8500 \end{bmatrix} \].