Mastering Break-Even Equations in Real-World Problems

A company sells t-shirts for $20 each and hoodies for $40 each. If the company wants to break even after spending $800 on production costs, how many t-shirts and hoodies must they sell?

• x + 2y = 40, where x is t-shirts and y is hoodies.

• 2x + y = 20

• x + 3y = 40

• x + y = 30

A bakery sells cupcakes for $3 each and cookies for $2 each. If the bakery's fixed costs are $150, how many cupcakes and cookies must they sell to break even?

• (60, 0)

• (25, 25)

• Any combination of cupcakes and cookies that satisfies 3x + 2y = 150, e.g., (50, 0) or (48, 3).

• (0, 75)

A gym charges a monthly fee of $50 and offers personal training sessions for $30 each. If the gym's monthly expenses are $1,200, how many members and personal training sessions must they have to break even?

• 24 members and 0 personal training sessions

• 15 members and 10 personal training sessions

• 30 members and 0 personal training sessions

• 20 members and 5 personal training sessions

A concert venue charges $25 per ticket and has fixed costs of $1,500. If they also sell VIP packages for $100 each, how many tickets and VIP packages must they sell to break even?

• 50 tickets and 5 VIP packages

• 30 tickets and 10 VIP packages

• 60 tickets and 0 VIP packages, or 0 tickets and 15 VIP packages, or any combination that satisfies 25t + 100v = 1500.

• 75 tickets and 2 VIP packages

A lemonade stand sells cups of lemonade for $2 and cookies for $1. If the total cost to set up the stand is $50, how many cups of lemonade and cookies must be sold to break even?

• 25 cups of lemonade and 0 cookies, or other combinations that satisfy 2x + y = 50.

• 20 cups of lemonade and 10 cookies

• 30 cups of lemonade and 5 cookies

• 10 cups of lemonade and 20 cookies

A video game store sells new games for $60 and used games for $30. If the store's monthly rent is $1,200, how many new and used games must they sell to break even?

• 15 new games or 30 used games

• 20 new games or 40 used games to break even.

• 30 new games or 60 used games

• 10 new games or 20 used games

A farmer sells apples for $1.50 per pound and oranges for $2.00 per pound. If the farmer's total costs are $300, how many pounds of apples and oranges must be sold to break even?

• 300 pounds of apples and 50 pounds of oranges

• 200 pounds of apples or 150 pounds of oranges, or any combination that satisfies 1.5a + 2o = 300.

• 250 pounds of apples or 100 pounds of oranges

• 100 pounds of apples and 100 pounds of oranges

A printing company charges $0.10 per page for black and white printing and $0.25 per page for color printing. If their monthly expenses are $500, how many pages of each type must they print to break even?

• x = 1500, y = 800

• x = 1800, y = 1500

• x = 2000, y = 1200

• x = 2500, y = 1000

A clothing store sells jeans for $50 and shirts for $25. If the store's total expenses are $2,000, how many jeans and shirts must they sell to break even?

• 30 jeans and 20 shirts

• 20 jeans and 40 shirts

• The store must sell 40 jeans and 0 shirts, or any combination that satisfies 50x + 25y = 2000.

• 10 jeans and 50 shirts

A local restaurant sells burgers for $10 and salads for $7. If their fixed costs are $1,000, how many burgers and salads must they sell to break even?

• 0 burgers and 150 salads

• 200 salads and 0 burgers

• 100 burgers and 0 salads (or other combinations that satisfy 10x + 7y = 1000)

• 50 burgers and 50 salads