Break Even Analysis: Solving Linear Equations for Profit

A company sells t-shirts for $20 each and hoodies for $40 each. If the fixed costs for the company are $200, how many t-shirts and hoodies must they sell to break even?

• 15 t-shirts and 0 hoodies

• 10 t-shirts and 0 hoodies, or 0 t-shirts and 5 hoodies, or any combination that satisfies 20x + 40y = 200.

• 5 t-shirts and 5 hoodies

• 0 t-shirts and 10 hoodies

A farmer sells apples for $2 per pound and oranges for $3 per pound. If the farmer's total costs are $120, how many pounds of each fruit must he sell to break even?

• 40 pounds of apples and 20 pounds of oranges

• 30 pounds of apples and 30 pounds of oranges

• 60 pounds of apples and 0 pounds of oranges (or other combinations like 54 apples and 4 oranges, etc.)

• 80 pounds of apples and 10 pounds of oranges

A gym charges a monthly fee of $30 and an additional $5 per class. If a member pays $80 in total, how many classes did they attend?

• 5

• 8

• 12

• 10

A concert venue has a fixed cost of $500 and charges $25 per ticket. How many tickets must be sold to cover the costs?

• 20

• 15

• 25

• 30

A bakery sells cupcakes for $3 each and cookies for $2 each. If the total revenue is $150 and they sold 50 items, how many of each item did they sell?

• 30 cupcakes and 20 cookies

• 20 cupcakes and 30 cookies

• 15 cupcakes and 35 cookies

• 25 cupcakes and 25 cookies

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, how many miles did they drive?

• 150 miles

• 200 miles

• 100 miles

• 50 miles

A school is selling tickets for a play at $10 each and for a raffle at $5 each. If they sold a total of 100 tickets for $600, how many of each type of ticket did they sell?

• 20 $10 tickets and 80 $5 tickets

• 50 $10 tickets and 50 $5 tickets

• 10 $10 tickets and 90 $5 tickets

• 30 $10 tickets and 70 $5 tickets

A mobile phone plan costs $40 per month plus $0.10 per text message. If a customer pays $60, how many text messages did they send?

• 150

• 200

• 250

• 100

A local theater sells adult tickets for $15 and child tickets for $10. If they sold a total of 200 tickets for $2,500, how many adult and child tickets were sold?

• 150 adult tickets and 50 child tickets

• 200 adult tickets and 0 child tickets

• 80 adult tickets and 120 child tickets

• 100 adult tickets and 100 child tickets

A delivery service charges a base fee of $15 plus $2 per mile. If a customer paid $35, how many miles did the delivery cover?

• 5 miles

• 10 miles

• 15 miles

• 20 miles