Solving Break Even Problems: Identify & Set Up Equations

A local bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery wants to break even after spending $120 on ingredients, how many cupcakes and cookies must they sell? Identify the variables and set up the equations.

• 50 cookies and 0 cupcakes

• The bakery must sell 40 cupcakes and 0 cookies, or any combination that satisfies the equation 3x + 2y = 120.

• 20 cupcakes and 20 cookies

• 30 cupcakes and 15 cookies

A concert hall has two types of tickets: regular tickets for $50 and VIP tickets for $100. If the total revenue from ticket sales is $2000, how many of each type of ticket were sold if 30 tickets were sold in total? Identify the variables and set up the equations.

• 10 regular tickets and 20 VIP tickets were sold.

• 20 regular tickets and 10 VIP tickets were sold.

• 15 regular tickets and 15 VIP tickets were sold.

• 25 regular tickets and 5 VIP tickets were sold.

A farmer sells apples for $1.50 per pound and oranges for $2.00 per pound. If he wants to make $300 from selling a total of 200 pounds of fruit, how many pounds of each fruit must he sell? Identify the variables and set up the equations.

• 100 pounds of apples and 100 pounds of oranges

• 200 pounds of apples and 0 pounds of oranges

• 150 pounds of apples and 50 pounds of oranges

• 0 pounds of apples and 200 pounds of oranges

A school is selling T-shirts for $15 each and hoodies for $30 each. If they want to raise $600 for a field trip, how many T-shirts and hoodies must they sell? Identify the variables and set up the equations.

• 10 T-shirts and 15 hoodies

• 20 T-shirts and 5 hoodies

• 30 T-shirts and 10 hoodies

• 40 T-shirts and 0 hoodies, or 0 T-shirts and 20 hoodies, or any combination that satisfies 15x + 30y = 600.

A company produces two types of gadgets: Type A for $25 each and Type B for $40 each. If they want to break even after spending $1000 on production costs, how many of each type must they sell if they plan to sell a total of 50 gadgets? Identify the variables and set up the equations.

• 30 Type A and 20 Type B gadgets

• 25 Type A and 25 Type B gadgets

• 40 Type A and 10 Type B gadgets

• 10 Type A and 40 Type B gadgets

A restaurant offers a lunch special for $10 and a dinner special for $20. If they want to make $500 in one day, how many lunch and dinner specials must they sell? Identify the variables and set up the equations.

• Sell 15 lunch specials and 20 dinner specials.

• Sell 20 lunch specials and 15 dinner specials.

• Sell 25 lunch specials and 10 dinner specials.

• Sell 30 lunch specials and 5 dinner specials.

A bookstore sells novels for $12 each and textbooks for $30 each. If they want to earn $720 from selling a total of 40 books, how many novels and textbooks must they sell? Identify the variables and set up the equations.

• 20 novels and 20 textbooks

• 15 novels and 25 textbooks

• 30 novels and 10 textbooks

• 26 novels and 14 textbooks

A car rental company charges $30 per day for a standard car and $50 per day for a luxury car. If they want to earn $600 in one week, how many of each type of car must they rent out? Identify the variables and set up the equations.

• They must rent 5 standard and 5 luxury cars.

• The problem cannot be solved with the given information alone.

• They need to rent 10 standard cars.

• They can only rent luxury cars to meet the goal.

A clothing store sells jeans for $40 and shirts for $20. If they want to make $800 in sales, how many jeans and shirts must they sell if they sell a total of 30 items? Identify the variables and set up the equations.

• 5 jeans and 25 shirts

• 15 jeans and 15 shirts

• 20 jeans and 10 shirts

• 10 jeans and 20 shirts