Break Even Solving Systems

The cost C (in dollars) for the care and maintenance of a horse and carriage is C=15x+2000, where x is the number of rides. They charge $35 per ride. How many rides are needed to break even?

• Approximately 57

• 133.333

• 100

• 40

A company's total cost is determined by the equation C=15x+150. Its revenue is determined by the equation R=45x. Find the break-even point in terms of x items sold.

• After 5 items sold, the company will have taken in zero dollars in revenue.

• After 5 items sold, the company will have made zero profit.

• After 3 items sold, the company will have taken in zero dollars in revenue.

• After 3 items sold, the company will have made zero dollars profit.

Is (-2,4) a solution to the system?

• Solution

• Not a solution

What is the break-even point in units for a company whose total fixed costs are $275,450; selling price per unit is $16; and variable cost per unit is $14.75?

• 220,360

• 150,300

• 183,633

• 225,120

At a local concert hall, the owner charges $7 per ticket. The owner must pay his band $1200. Every customer receives a brochure that costs the owner $2 for each person.

What system would determine when he breaks even?

• y = 7x

  y = 2x + 1200

• y = 2x

  y = 7x + 1200

• y = 9x + 1200

• y = -2x - 1200

  y = 7x

(a)  

• A

• B

• C

• D

Alex and Billy are running laps. According to the graph, how long will it take for the two boys to run the same distance?

• 20 minutes

• 15 minutes

• 10 minutes

• 5 minutes

Ride and Transport are two new ride sharing companies in Colorado. Ride is charging $2 for pick up fees and then $2.50 per mile. Transport is charging only $2.70 per mile. How many miles will it take for both companies to charge the same amount? Write a system of equations to solve.

• 27 miles

• 10 miles

• 270 miles

• 100 miles

Your friend rents 10 chairs and 2 tables for $300. Another friend rents 8 chairs and 4 tables for $360. How much does a chair and a table cost? Write a system of equations to solve.

• Chairs $2 Tables $5

• Chairs $50 Tables $20

• Chairs $10 Tables $15

• Chairs $20 Tables $50

You and your brother each decide to open a savings account. You open your account at Elsa’s Banking Branch. Your brother opens his account at Anna’s Banking Company. You put $50 in the bank and your account earns $4 per week in interest. Your brother puts $150 in his account but only earns $2 per week in interest. How many weeks will it take for both your brother and your account to have the same balance? Write a system of linear equations to solve the problem.

• 200 weeks

• 300 weeks

• 50 weeks

• 250 weeks