Linear & Quadratic Equations: Real-World Challenges

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer drives a total of 150 miles, how much will they pay? Write a linear equation to represent the total cost and solve it.

• $80

• $70

• $100

• $90

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 54 square meters, find the dimensions of the garden using a quadratic equation.

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 1.75 seconds

• 2.24 seconds

• 4.50 seconds

• 3.10 seconds

Two friends, Alice and Bob, are saving money for a concert. Alice saves $5 each week, while Bob saves $3 each week. If Alice has $20 more than Bob after a certain number of weeks, write a system of equations to represent their savings and solve for the number of weeks.

• 10 weeks

• 15 weeks

• 5 weeks

• 12 weeks

A rectangular pool is being built with a length that is twice its width. If the area of the pool is 200 square meters, find the dimensions of the pool using a quadratic equation.

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. Determine the time at which the projectile reaches its maximum height.

• 3 seconds

• 1 second

• 2 seconds

• 0.5 seconds

A store sells two types of shirts: plain shirts for $15 each and graphic shirts for $25 each. If a customer buys a total of 10 shirts for $200, write a system of equations to represent the situation and solve for the number of each type of shirt purchased.

• 6 plain shirts and 4 graphic shirts

• 8 plain shirts and 2 graphic shirts

• 5 plain shirts and 5 graphic shirts

• 7 plain shirts and 3 graphic shirts

A farmer has a rectangular field that is 4 meters longer than it is wide. If the perimeter of the field is 48 meters, find the dimensions of the field using a system of equations.

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

• Width: 12 meters, Length: 16 meters

The sum of two numbers is 30, and their product is 216. Write a system of equations to represent the situation and solve for the two numbers using quadratic equations.

• 10 and 20

• 15 and 15

• The two numbers are 18 and 12.

• 24 and 6

A train travels 60 miles per hour and leaves a station at the same time as a car that travels 45 miles per hour. If the train is 30 miles ahead of the car when they start, how long will it take for the car to catch up to the train? Write and solve a linear equation to find the time.

• 4 hours

• 3 hours

• 2 hours

• 1 hour