Graphing and Analyzing Systems of Equations in Word Problems

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 50 tickets for $400, how many adult and student tickets were sold? Set up the system of equations and graph it.

• 25 adult tickets and 25 student tickets were sold.

• 40 adult tickets and 10 student tickets were sold.

• 35 adult tickets and 15 student tickets were sold.

• 30 adult tickets and 20 student tickets were sold.

Maria has a total of 30 coins consisting of dimes and quarters. If the total value of the coins is $5.50, how many dimes and quarters does she have? Set up the system of equations and analyze the requirements.

• 5 dimes and 25 quarters

• Maria has 13 dimes and 17 quarters.

• 15 dimes and 15 quarters

• 10 dimes and 20 quarters

A farmer has chickens and cows. The total number of animals is 40, and the total number of legs is 120. How many chickens and cows does the farmer have? Set up the system of equations and graph it.

• 10 chickens and 30 cows

• 20 chickens and 20 cows

• 15 chickens and 25 cows

• 25 chickens and 15 cows

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 a week, while Jamie saves $10 a week. If Alex has $30 more than Jamie after a certain number of weeks, how many weeks will it take for them to have the same amount saved? Set up the system of equations and analyze the requirements.

• 10 weeks

• 8 weeks

• 4 weeks

• 6 weeks

A store sells two types of bicycles: mountain bikes for $200 and road bikes for $150. If the store sold a total of 60 bikes for $10,500, how many of each type were sold? Set up the system of equations and graph it.

• 40 mountain bikes and 20 road bikes were sold.

• 15 mountain bikes and 45 road bikes were sold.

• 20 mountain bikes and 40 road bikes were sold.

• 30 mountain bikes and 30 road bikes were sold.

In a class, there are boys and girls. The total number of students is 24, and there are 10 more girls than boys. How many boys and girls are in the class? Set up the system of equations and analyze the requirements.

• 7 boys and 17 girls

• 8 boys and 16 girls

• 10 boys and 14 girls

• 5 boys and 19 girls

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70 for their rental, how many miles did they drive? Set up the system of equations and graph it.

• 200 miles

• 50 miles

• 150 miles

• 100 miles

A local bakery sells muffins and cookies. Each muffin costs $2 and each cookie costs $1. If they sold a total of 100 items for $150, how many muffins and cookies were sold? Set up the system of equations and analyze the requirements.

• 30 muffins and 70 cookies

• 50 muffins and 50 cookies

• 60 muffins and 40 cookies

• 40 muffins and 60 cookies

A concert hall has two types of seating: regular seats for $25 and VIP seats for $50. If they sold a total of 200 seats for $7,500, how many regular and VIP seats were sold? Set up the system of equations and graph it.

• 200 regular seats and 0 VIP seats were sold.

• 100 regular seats and 100 VIP seats were sold.

• 50 regular seats and 150 VIP seats were sold.

• 150 regular seats and 50 VIP seats were sold.

In a fruit market, apples cost $3 per pound and bananas cost $2 per pound. If a customer buys a total of 10 pounds of fruit for $24, how many pounds of apples and bananas did they buy? Set up the system of equations and analyze the requirements.

• 5 pounds of apples and 5 pounds of bananas

• 4 pounds of apples and 6 pounds of bananas

• 2 pounds of apples and 8 pounds of bananas

• 3 pounds of apples and 7 pounds of bananas