Graphing and Analyzing Systems of Equations in Context

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 in slope-intercept form and graph them to find the solution.

• 30 cupcakes and 10 cookies

• Any combination of cupcakes and cookies that satisfies 2x + y = 50, e.g., 25 cupcakes and 0 cookies, or 0 cupcakes and 50 cookies.

• 5 cupcakes and 45 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? Graph the equations to find the solution.

• 200 miles

• 150 miles

• 250 miles

• 100 miles

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 if they want to stay within budget? Write and graph the equations to find the solution.

• 12

• 20

• 15

• 10

Two friends are saving money to buy a video game. Friend A saves $5 a week, while Friend B saves $3 a week. If Friend A starts with $20 and Friend B starts with $10, how many weeks will it take for them to have the same amount saved? Graph the equations to find the solution.

• 10 weeks

• 7 weeks

• 5 weeks

• 3 weeks

A gym charges a monthly fee of $40 plus $5 per class attended. Another gym charges a flat fee of $50 with no additional class fees. How many classes must you attend for the costs to be the same? Write the equations in slope-intercept form and graph them to find the solution.

• 1

• 3

• 4

• 2

A farmer has a total of 100 animals consisting of cows and chickens. If cows are counted as 2 animals and chickens as 1, how many of each type of animal does the farmer have if he wants to maximize the number of cows? Graph the equations to find the solution.

• 0 cows and 100 chickens

• 50 cows and 50 chickens

• 75 cows and 25 chickens

• 100 cows and 0 chickens

A concert venue sells tickets for $25 each and VIP passes for $50 each. If they want to make $2000 in total sales, how many tickets and VIP passes do they need to sell? Write the equations in slope-intercept form and graph them to find the solution.

• 40 tickets and 30 VIP passes

• 100 tickets and 10 VIP passes

• They need to sell 80 tickets and 0 VIP passes, or any combination that satisfies 25x + 50y = 2000.

• 60 tickets and 20 VIP passes

A phone company offers two plans: Plan A costs $30 per month plus $0.10 per text, while Plan B costs $20 per month plus $0.15 per text. How many texts must you send for the costs to be the same? Graph the equations to find the solution.

• 250

• 200

• 300

• 150

A bookstore sells novels for $15 each and textbooks for $30 each. If they want to earn $600 in sales, how many novels and textbooks do they need to sell? Write the equations in slope-intercept form and graph them to find the solution.

• (10 novels, 20 textbooks)

• The bookstore can sell combinations of novels and textbooks such as (0 novels, 20 textbooks), (10 novels, 15 textbooks), (20 novels, 10 textbooks), (30 novels, 5 textbooks), or (40 novels, 0 textbooks) to reach $600 in sales.

• (25 novels, 0 textbooks)

• (5 novels, 15 textbooks)

A pizza shop sells small pizzas for $10 and large pizzas for $15. If they want to make $300 in sales, how many small and large pizzas do they need to sell? Graph the equations to find the solution.

• (20, 0)

• (5, 15)

• Any combination of small and large pizzas that satisfies 10x + 15y = 300, such as (0, 20) or (15, 0).

• (10, 10)