Solving Real-World Problems with Linear & Quadratic Equations

A farmer has a rectangular field with a length that is 3 meters longer than its width. If the area of the field is 70 square meters, what are the dimensions of the field?

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.30 per mile. How many miles must you drive for both companies to charge the same amount?

• 200 miles

• 150 miles

• 250 miles

• 100 miles

A ball is thrown into the air, and its height in meters can be modeled by the equation h(t) = -4.9t^2 + 20t + 1, where t is the time in seconds. At what time will the ball hit the ground?

• 3.5 seconds

• 5.0 seconds

• 4.12 seconds

• 2.8 seconds

A concert hall has a seating capacity of 500. If tickets are sold for $20 each, the hall sells out. However, for every $2 increase in ticket price, 10 fewer tickets are sold. What ticket price maximizes revenue?

• $80

• $68

• $100

• $50

A rectangular garden has a length that is twice its width. If the perimeter of the garden is 48 meters, what are the dimensions of the garden?

• Width: 12 meters, Length: 24 meters

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 20 meters

• Width: 6 meters, Length: 12 meters

A company produces two types of gadgets. The profit from the first type is modeled by the equation P1(x) = 5x - 10, and the profit from the second type is modeled by P2(y) = -2y^2 + 12y - 8. How many of each type should the company produce to maximize profit?

• 3 of the first type and 2 of the second type

• 2 of the first type and 3 of the second type

• 1 of the first type and 4 of the second type

• 0 of the first type and 5 of the second type

A train travels at a constant speed of 60 km/h. A car leaves the same station 30 minutes later and travels at 90 km/h. How far from the station will the car catch up to the train?

• 90 km

• 75 km

• 120 km

• 60 km

A rectangular swimming pool is 4 meters longer than it is wide. If the area of the pool is 96 square meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

A local bakery sells cupcakes for $3 each and cookies for $2 each. If the total revenue from selling 100 items is $240, how many cupcakes and cookies were sold?

• 20 cupcakes and 80 cookies

• 40 cupcakes and 60 cookies

• 50 cupcakes and 50 cookies

• 30 cupcakes and 70 cookies

A quadratic function models the height of a projectile. If the function is given by h(t) = -16t^2 + 64t + 48, at what time does the projectile reach its maximum height?

• 4 seconds

• 1 second

• 3 seconds

• 2 seconds