Solving Real-World Problems with Systems of Equations

A local bakery sells cupcakes for $2 each and cookies for $1 each. If they want to make $50 in sales, how many cupcakes and cookies do they need to sell? Write the equations and find the intersection point.

• Multiple combinations, e.g., 20 cupcakes and 10 cookies.

• 25 cookies and 0 cupcakes

• 15 cupcakes and 5 cookies

• 10 cupcakes and 20 cookies

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $20 plus $0.25 per mile. How many miles must you drive for the costs to be the same? Write the equations and interpret the intersection point.

• 100 miles

• 150 miles

• 250 miles

• 200 miles

A school is planning a field trip. The cost per student is $15 for a bus that holds 30 students and $10 for a bus that holds 20 students. How many students need to go for the costs to be equal? Write the equations and find the intersection point.

• 75

• 60

• 30

• 45

A phone company offers a plan for $40 a month with unlimited texting and $0.10 per text. Another plan costs $30 a month with $0.15 per text. How many texts would make the plans cost the same? Write the equations and interpret the intersection point.

• 250

• 200

• 150

• 300

A farmer has two types of crops. Crop A yields $200 per acre and Crop B yields $150 per acre. If he wants to earn $6000, how many acres of each crop should he plant? Write the equations and find the intersection point.

• 20 acres of Crop A and 10 acres of Crop B

• The farmer can plant 30 acres of Crop A and 0 acres of Crop B, or 0 acres of Crop A and 40 acres of Crop B.

• 15 acres of Crop A and 15 acres of Crop B

• 25 acres of Crop A and 5 acres of Crop B

A gym charges a monthly fee of $25 plus $5 per class. Another gym charges a flat fee of $40 with no class fees. How many classes must you take for the costs to be equal? Write the equations and interpret the intersection point.

• 5

• 3

• 4

• 2

A concert venue sells tickets for $50 each and VIP passes for $100 each. If they want to make $2000 in ticket sales, how many of each type of ticket must they sell? Write the equations and find the intersection point.

• 30 tickets and 10 VIP passes

• 20 tickets and 20 VIP passes

• 50 tickets and 0 VIP passes

• 40 tickets and 0 VIP passes (x=40, y=0)

A delivery service charges $10 for the first mile and $2 for each additional mile. Another service charges $5 for the first mile and $3 for each additional mile. How far must you go for the costs to be the same? Write the equations and interpret the intersection point.

• 6 miles

• 4 miles

• 8 miles

• 10 miles

A bookstore sells novels for $15 each and textbooks for $30 each. If they want to make $300 in sales, how many novels and textbooks do they need to sell? Write the equations and find the intersection point.

• 5 novels and 10 textbooks

• 15 novels and 5 textbooks

• 20 novels and 0 textbooks, or 10 novels and 5 textbooks, or 0 novels and 10 textbooks.

• 25 novels and 0 textbooks

A restaurant offers a lunch special for $10 and a dinner special for $20. If they want to make $500 in sales, how many lunch and dinner specials do they need to sell? Write the equations and interpret the intersection point.

• 30 lunch specials and 5 dinner specials

• 10 lunch specials and 20 dinner specials

• 15 lunch specials and 10 dinner specials

• To achieve $500 in sales, they can sell 25 lunch specials and 0 dinner specials, or 20 lunch specials and 5 dinner specials, among other combinations.