Solving Real-Life Problems with Matrices and Equations

A school is organizing a trip for 120 students. The cost per student is $50 for transportation and $30 for meals. Create a matrix to represent the total cost for transportation and meals for all students. What is the total cost?

• $8000

• $9600

• $7200

• $12000

A company produces two types of gadgets, A and B. The production of gadget A requires 3 hours of labor and gadget B requires 2 hours. If the company has 60 hours of labor available, set up a system of equations to determine how many of each gadget can be produced if they want to maximize production.

• The company can produce a maximum of 15 gadgets A and 10 gadgets B.

• The company can produce a maximum of 10 gadgets A and 20 gadgets B.

• The company can produce a maximum of 25 gadgets A and 5 gadgets B.

• The company can produce a maximum of 20 gadgets A and 0 gadgets B, or 0 gadgets A and 30 gadgets B, or any combination that satisfies 3x + 2y <= 60.

In a bakery, the ratio of chocolate cakes to vanilla cakes is 3:2. If there are 50 cakes in total, represent this situation with a matrix and find the number of each type of cake.

• 25 chocolate cakes and 25 vanilla cakes

• 30 chocolate cakes and 20 vanilla cakes

• 40 chocolate cakes and 10 vanilla cakes

• 15 chocolate cakes and 35 vanilla cakes

A farmer has a total of 100 animals, consisting of cows and chickens. If cows are counted as 2 and chickens as 1 in terms of animal units, set up a matrix to represent the situation and find the number of cows and chickens if there are 40 animal units.

• 60 cows and 40 chickens

• 70 cows and 30 chickens

• 50 cows and 50 chickens

• 80 cows and 20 chickens

A concert hall has two types of seating: regular and VIP. The total number of seats is 200, and the revenue from regular seats is $20 each while VIP seats are $50 each. Create a matrix to represent the revenue and find the number of each type of seat sold if the total revenue is $7000.

• 150 regular seats and 50 VIP seats

• 200 regular seats and 0 VIP seats

• 100 regular seats and 100 VIP seats

• 50 regular seats and 150 VIP seats

A store sells two types of shirts: plain and printed. The store has a total of 150 shirts, and the ratio of plain to printed shirts is 4:1. Set up a system of equations to find the number of each type of shirt.

• 90 plain shirts and 60 printed shirts

• 100 plain shirts and 50 printed shirts

• 75 plain shirts and 75 printed shirts

• 120 plain shirts and 30 printed shirts

In a sports league, Team A won 3 times as many games as Team B. If the total number of games won by both teams is 40, create a matrix to represent the situation and find the number of games won by each team.

• Team A won 35 games and Team B won 5 games.

• Team A won 25 games and Team B won 15 games.

• Team A won 20 games and Team B won 20 games.

• Team A won 30 games and Team B won 10 games.

A delivery service has two types of packages: small and large. The small package costs $5 to deliver and the large package costs $10. If the total delivery cost for 30 packages is $200, set up a system of equations to find the number of each type of package delivered.

• 10 small packages and 20 large packages

• 20 small packages and 10 large packages

• 15 small packages and 15 large packages

• 25 small packages and 5 large packages

A school is conducting a survey on students' favorite subjects: Math, Science, and English. The results show that 40 students prefer Math, 30 prefer Science, and 50 prefer English. Create a matrix to represent the preferences and find the total number of students surveyed.

• 110

• 120

• 100

• 130

A factory produces two products, X and Y. Each product X requires 2 hours of machine time and product Y requires 3 hours. If the factory has 24 hours available, set up a system of equations to determine the maximum number of products that can be produced.

• 8

• 12

• 6

• 10