Graphing and Solving Systems of Equations in Real Life

A farmer has 100 meters of fencing to create a rectangular pen for his animals. If the length of the pen is represented by the equation y = 50 - x, where x is the width, graph the system of equations to find the dimensions that maximize the area.

• 25 meters by 25 meters

• 20 meters by 30 meters

• 40 meters by 10 meters

• 30 meters by 20 meters

A school is planning a field trip and has a budget of $300. The cost per student is represented by the equation y = 15x, and the total number of students is represented by the equation y = 300 - 10x. Graph the system of equations to determine how many students can attend the trip.

• 12

• 20

• 10

• 15

Two friends are selling lemonade and cookies. The equation for the total money made from lemonade is y = 2x, and for cookies, it is y = 3x - 5. Graph the equations to find out how many of each item they need to sell to make the same amount of money.

• 5 lemonade and 5 cookies

• 4 lemonade and 6 cookies

• 10 lemonade and 2 cookies

• 3 lemonade and 7 cookies

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. The equation for the total cost is y = 0.2x + 50. Another company charges $30 plus $0.25 per mile. Write the equation for the second company and graph both to find when the costs are equal.

• The costs are equal at 20 miles for a total cost of $50.

• The costs are equal at 60 miles for a total cost of $70.

• The costs are equal at 30 miles for a total cost of $55.

• The costs are equal at 40 miles for a total cost of $58.

A concert venue has two pricing models for tickets. The first model is represented by the equation y = 20x, and the second model is y = 15x + 30. Graph the equations to find out how many tickets need to be sold for both models to earn the same revenue.

• 6

• 4

• 10

• 8

A local gym offers two membership plans. The first plan costs $40 per month, and the second plan has a $20 sign-up fee plus $30 per month. Write the equations for both plans and graph them to find out when the costs are equal over time.

• The costs are equal after 1 month.

• The costs are equal after 4 months.

• The costs are equal after 2 months.

• The costs are equal after 3 months.

A bookstore sells novels for $10 each and textbooks for $15 each. The equation for the total sales from novels is y = 10x, and for textbooks, it is y = 15x - 30. Graph the equations to determine how many novels and textbooks need to be sold to achieve the same sales amount.

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

• 7 novels and 3 textbooks

• 5 novels and 5 textbooks

A delivery service charges a base fee of $5 plus $1.50 per mile. The equation for the total cost is y = 1.5x + 5. Another service charges a flat fee of $10. Write the equation for the second service and graph both to find when the costs are equal.

• The costs are equal at 2 miles.

• The costs are equal at 5 miles.

• The costs are equal at approximately 3.33 miles.

• The costs are equal at 1.5 miles.

A bakery sells cupcakes for $3 each and cookies for $2 each. The equation for the total sales from cupcakes is y = 3x, and for cookies, it is y = 2x + 10. Graph the equations to find out how many cupcakes and cookies need to be sold to earn the same amount.

• 15 cupcakes and 5 cookies

• 5 cupcakes and 15 cookies

• 20 cupcakes and 5 cookies

• 10 cupcakes and 10 cookies

A charity organization is selling raffle tickets for $5 each and donations for $10 each. The equation for the total money from tickets is y = 5x, and for donations, it is y = 10x - 20. Graph the equations to find out how many tickets and donations are needed to raise the same amount of money.

• 2 tickets and 4 donations

• 6 tickets and 1 donation

• 4 tickets and 2 donations

• 3 tickets and 5 donations