Solving Real-World Problems: Linear Equations Quiz

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is 10 meters more than the width, what are the dimensions of the pen? Use substitution to solve the system of equations.

• Width: 15 meters, Length: 25 meters

• Width: 20 meters, Length: 30 meters

• Width: 30 meters, Length: 40 meters

• Width: 25 meters, Length: 35 meters

A school is planning a field trip and has a budget of $300. The cost per student is $15 for transportation and $10 for admission. How many students can attend the trip if the school wants to spend all of its budget? Use elimination to solve the system of equations.

• 20

• 15

• 12

• 10

Two friends, Alex and Jamie, are selling lemonade and cookies at a local fair. Alex sells lemonade for $2 per cup and cookies for $1 each, while Jamie sells lemonade for $3 per cup and cookies for $2 each. If they both made $50 in total, how many cups of lemonade and cookies did each sell? Use substitution to solve the system of equations.

• Alex sells 20 cups of lemonade and 0 cookies; Jamie sells 0 cups of lemonade and 10 cookies.

• Alex sells 15 cups of lemonade and 10 cookies; Jamie sells 5 cups of lemonade and 5 cookies.

• Alex sells 5 cups of lemonade and 30 cookies; Jamie sells 5 cups of lemonade and 5 cookies.

• Alex sells 10 cups of lemonade and 20 cookies; Jamie sells 0 cups of lemonade and 0 cookies.

A concert hall has a seating capacity of 500. If the number of rows is 20 and each row has the same number of seats, how many seats are in each row? Use elimination to solve the system of equations.

• 25

• 15

• 20

• 30

A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 10 items and spends $80, how many novels and magazines did they buy? Use substitution to solve the system of equations.

• 5 novels and 5 magazines

• 3 novels and 7 magazines

• 4 novels and 6 magazines

• 6 novels and 4 magazines

A local gym offers two types of memberships: a monthly membership for $30 and a yearly membership for $300. If a customer wants to spend exactly $600 on memberships, how many of each type did they purchase? Use elimination to solve the system of equations.

• 1 monthly, 1 yearly

• 0 monthly, 2 yearly

• 2 monthly, 1 yearly

• 3 yearly, 0 monthly

In a school, the ratio of boys to girls is 3:2. If there are 50 students in total, how many boys and girls are there? Use substitution to solve the system of equations.

• 40 boys and 10 girls

• 25 boys and 25 girls

• 30 boys and 20 girls

• 35 boys and 15 girls

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70 for their rental, how many miles did they drive? Use elimination to solve the system of equations.

• 200 miles

• 100 miles

• 50 miles

• 150 miles

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 15 items and spends $36, how many cupcakes and cookies did they buy? Use substitution to solve the system of equations.

• 7 cupcakes and 8 cookies

• 6 cupcakes and 9 cookies

• 5 cupcakes and 10 cookies

• 4 cupcakes and 11 cookies

A charity event sold tickets for $10 each and received a total of $500 from ticket sales. If they sold 20 more tickets than the number of $10 tickets, how many tickets did they sell in total? Use elimination to solve the system of equations.

• 50

• 70

• 60

• 80