Graphing Systems of Equations: Costs & Comparisons

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write the equation in slope-intercept form and determine how many miles you can drive if your total cost is $50. Interpret the solution graphically.

• 50 miles

• 100 miles

• 120 miles

• 75 miles

Two friends, Alex and Jamie, are selling lemonade. Alex sells lemonade for $2 per cup, while Jamie sells it for $3 per cup. Write the equations for their sales and find the point where their sales are equal. What does this point represent graphically?

• The point where their sales are equal is (0, 0).

• The point where their sales are equal is (1, 2).

• The point where their sales are equal is (3, 5).

• The point where their sales are equal is (2, 3).

A school is planning a field trip. The cost per student is $15 for transportation and $5 for lunch. Write the equation for the total cost in slope-intercept form. If the total cost is $200, how many students are going?

• 10 students

• 20 students

• 15 students

• 5 students

Two lines are represented by the equations y = 2x + 3 and y = -0.5x + 1. Are these lines parallel, perpendicular, or neither? Explain your reasoning using their slopes.

• coincident

• parallel

• intersecting

• perpendicular

A farmer has two types of crops. He sells corn for $4 per bushel and wheat for $3 per bushel. If he sells a total of 100 bushels for $360, write a system of equations to represent this situation and find the number of bushels of each crop sold. Interpret the solution graphically.

• 80 bushels of corn and 20 bushels of wheat

• 50 bushels of corn and 50 bushels of wheat

• 70 bushels of corn and 30 bushels of wheat

• 60 bushels of corn and 40 bushels of wheat

Two lines are given by the equations y = 3x + 2 and y = 3x - 4. Are these lines parallel, perpendicular, or neither? Justify your answer by analyzing their slopes.

• The lines are perpendicular.

• The lines intersect at one point.

• The lines have different slopes.

• The lines are parallel.

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer buys a total of 10 books for $160, write a system of equations to find out how many of each type of book was purchased. How would you graph this situation?

• 5 novels and 5 textbooks

• 3 novels and 7 textbooks

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

A concert venue has two pricing models: one charges $50 per ticket and the other charges $30 plus a $20 service fee. Write the equations for both models and find the point where the total costs are equal. What does this point signify in the context of the problem?

• 1 ticket sold

• 2 tickets sold

• $30 per ticket

• $50 service fee