Matrix Addition and Subtraction in Real-World Scenarios

A bakery produces two types of cakes: chocolate and vanilla. In one day, they made 30 chocolate cakes and 20 vanilla cakes. Represent this situation with a matrix. If they decide to make 10 more chocolate cakes and 5 more vanilla cakes, what is the resulting matrix after addition?

• [[35], [25]]

• [[30], [20]]

• [[40], [20]]

• [[40], [25]]

A school has two classes, Class A and Class B. Class A has 25 students and Class B has 30 students. Represent the number of students in each class as a matrix. If 5 students from Class A transfer to Class B, what is the new matrix representing the number of students in each class?

• [[30], [25]]

• [[20], [30]]

• [[25], [30]]

• [[20], [35]]

A car rental company has two types of cars: sedans and SUVs. They have 15 sedans and 10 SUVs available. If they rent out 3 sedans and 2 SUVs, represent the initial and final number of cars as matrices and find the difference using matrix subtraction.

• The difference in the number of cars is \[ \begin{bmatrix} 12 & 8 \end{bmatrix} \].

• The difference in the number of cars is \[ \begin{bmatrix} 10 & 5 \end{bmatrix} \].

• The difference in the number of cars is \[ \begin{bmatrix} 3 & 2 \end{bmatrix} \].

• The difference in the number of cars is \[ \begin{bmatrix} 5 & 3 \end{bmatrix} \].

A factory produces two products: widgets and gadgets. In one week, they produced 100 widgets and 150 gadgets. If they increase production by 20 widgets and 30 gadgets the next week, represent both weeks' production as matrices and find the total production using matrix addition.

• 110 widgets and 160 gadgets.

• 100 widgets and 150 gadgets.

• 130 widgets and 200 gadgets.

• Total production: 120 widgets and 180 gadgets.

A sports team has two types of players: forwards and defenders. They have 12 forwards and 8 defenders. If they recruit 4 more forwards and 2 more defenders, represent the initial and final number of players as matrices and calculate the change using matrix addition.

• [[12], [8]] + [[3], [1]] = [[15], [9]]

• [[12], [8]] + [[4], [4]] = [[16], [12]]

• [[12], [8]] + [[4], [2]] = [[16], [10]]

• [[10], [6]] + [[5], [3]] = [[15], [9]]

A delivery service has two routes: Route 1 and Route 2. Route 1 has 40 packages and Route 2 has 60 packages. If they deliver 10 packages from Route 1 and 15 from Route 2, represent the initial and final number of packages as matrices and find the difference using matrix subtraction.

• [[30], [35]]

• [[5], [10]]

• [[10], [15]]

• [[20], [25]]

A bookstore has two sections: fiction and non-fiction. They have 50 fiction books and 30 non-fiction books. If they sell 5 fiction books and 10 non-fiction books, represent the initial and final inventory as matrices and calculate the change using matrix subtraction.

• [[10], [5]]

• [[5], [5]]

• [[0], [10]]

• [[5], [10]]

A gym has two types of memberships: basic and premium. They have 100 basic members and 50 premium members. If they gain 20 new basic members and lose 5 premium members, represent the initial and final membership counts as matrices and find the total using matrix addition.

• 165

• 175

• 160

• 150

A concert venue has two sections: VIP and General Admission. They have 200 VIP tickets and 300 General Admission tickets. If they sell 50 VIP tickets and 100 General Admission tickets, represent the initial and final ticket counts as matrices and calculate the change using matrix subtraction.

• [[150], [200]]

• [[50], [200]]

• [[100], [150]]

• [[50], [100]]

A clothing store has two types of clothing: shirts and pants. They have 80 shirts and 40 pants. If they receive a shipment of 20 shirts and 10 pants, represent the initial and final inventory as matrices and find the total using matrix addition.

• Final inventory matrix: [[90], [45]]

• Final inventory matrix: [[120], [60]]

• Final inventory matrix: [[100], [50]]

• Final inventory matrix: [[80], [40]]