Solving Real-World Problems with Nonlinear Systems

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, find the dimensions of the field using a system of nonlinear equations.

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 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 $0.25 per mile. How many miles must you drive for the costs to be the same? Use a system of nonlinear equations to solve.

• 400 miles

• 500 miles

• 300 miles

• 200 miles

Two friends are running a race. The first friend runs at a speed of 5 meters per second, while the second friend runs at a speed of 3 meters per second. If the first friend has a 10-meter head start, how long will it take for the second friend to catch up? Set up a system of nonlinear equations to find the answer.

• 10 seconds

• 5 seconds

• 7 seconds

• 3 seconds

A rectangular garden has a length that is twice its width. If the perimeter of the garden is 48 meters, find the dimensions of the garden using a system of nonlinear equations.

• Length: 12 meters, Width: 6 meters

• Length: 24 meters, Width: 12 meters

• Length: 16 meters, Width: 8 meters

• Length: 20 meters, Width: 10 meters

A company produces two types of gadgets. The first type costs $20 to produce, and the second type costs $30. If the company has a budget of $600 and wants to produce a total of 25 gadgets, how many of each type can they produce? Use a system of nonlinear equations to solve.

• 15 type 1 gadgets and 10 type 2 gadgets

• 10 type 1 gadgets and 15 type 2 gadgets

• 5 type 1 gadgets and 20 type 2 gadgets

• 20 type 1 gadgets and 5 type 2 gadgets

A swimming pool is being filled with water. The pool can hold 5000 liters, and water is being added at a rate of 100 liters per hour. If the pool is currently half full, how long will it take to fill the pool completely? Use a system of nonlinear equations to find the time.

• 20 hours

• 30 hours

• 15 hours

• 25 hours

A local bakery sells two types of cakes: chocolate and vanilla. The chocolate cakes cost $15 each, and the vanilla cakes cost $10 each. If the bakery made a total of 30 cakes and earned $400, how many of each type of cake did they sell? Set up a system of nonlinear equations to solve this problem.

• 10 chocolate cakes and 20 vanilla cakes

• 20 chocolate cakes and 10 vanilla cakes

• 15 chocolate cakes and 15 vanilla cakes

• 25 chocolate cakes and 5 vanilla cakes

A cyclist travels 10 kilometers at a speed of 15 km/h and then returns at a speed of 10 km/h. How long does the entire trip take? Use a system of nonlinear equations to analyze the scenario and find the total time.

• 1.50 hours

• 2.00 hours

• 1.67 hours

• 1.25 hours

A school is planning a field trip and has a budget of $1200. The cost per student is $30 for transportation and $20 for admission. If 40 students are going, will they stay within budget? Use a system of nonlinear equations to analyze the costs.

• Yes, they will stay within budget.

• They will stay within budget with $200 left.

• No, they will not stay within budget.

• They will exceed the budget by $100.

A store sells two types of shirts: cotton and polyester. The cotton shirts cost $25 each, and the polyester shirts cost $20 each. If the store sold a total of 100 shirts and made $2200, how many of each type did they sell? Use a system of nonlinear equations to find the answer.

• 40 cotton shirts and 60 polyester shirts

• 20 cotton shirts and 80 polyester shirts

• 50 cotton shirts and 50 polyester shirts

• 30 cotton shirts and 70 polyester shirts