Mastering Systems of Equations: Slope & Intercept Challenges

A local bakery sells cupcakes for $2 each and cookies for $3 each. If they made a total of $60 from selling cupcakes and cookies, and sold 10 more cupcakes than cookies, what are the equations representing this situation?

• 2x + 3(x + 10) = 60 and x + 10 = cookies, where x = cupcakes.

• 3x + 2x = 60 and x = cookies, where x = cupcakes.

• 3x + 2(x + 10) = 60 and x + 10 = cupcakes, where x = cookies.

• 2x + 3(x - 10) = 60 and x - 10 = cookies, where x = cupcakes.

A school is planning a field trip and has a budget of $300. The cost per student for the bus is $15, and the cost per student for admission is $20. If 10 more students attend than the number of buses rented, what are the equations that model this scenario?

• x + 10 = number of students; 35(x + 10) = 300

• x + 15 = number of students; 20(x + 15) = 300

• x + 5 = number of students; 25(x + 5) = 300

• x + 10 = number of students; 30(x + 10) = 300

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 each week, while Jamie saves $8 each week. If Alex has $20 saved already and Jamie has $12, how can you represent their savings with equations?

• A = 20 + 8w, J = 12 + 5w

• A = 20 + 5w, J = 12 + 8w

• A = 5w, J = 8w

• A = 20 - 5w, J = 12 - 8w

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.25 per mile. How can you write the equations for the total cost for each company, and at what mileage do the costs become equal?

• 300 miles

• 500 miles

• 350 miles

• 400 miles

A farmer has a total of 100 animals, consisting of chickens and cows. If there are 3 times as many chickens as cows, how can you express this situation with a system of equations?

• x + y = 100, x = 3y

• x + 3y = 100, y = x

• x + y = 100, y = 3x

• 3x + y = 100, y = 3x

A movie theater sells adult tickets for $10 and child tickets for $5. If they sold a total of 150 tickets and made $1,200, what equations can you create to represent the number of adult and child tickets sold?

• x + y = 150; 10x + 5y = 1500

• x + y = 100; 10x + 5y = 1000

• x + y = 200; 10x + 5y = 1500

• x + y = 150; 10x + 5y = 1200

In a school, the number of boys is twice the number of girls. If the total number of students is 60, how can you set up a system of equations to find the number of boys and girls?

• There are 20 girls and 40 boys.

• 30 girls and 30 boys.

• 10 girls and 50 boys.

• 25 girls and 35 boys.

A gym charges a monthly fee of $30 plus $5 per class attended. Another gym charges a flat fee of $20 plus $8 per class. How can you write the equations for the total cost for each gym, and how can you determine when the costs are the same?

• The equations are C1 = 30 + 5x and C2 = 20 + 8x. The costs are the same when x = 10/3 classes.

• C1 = 30 + 8x and C2 = 20 + 5x; costs are the same when x = 5 classes.

• C1 = 25 + 5x and C2 = 20 + 10x; costs are the same when x = 2 classes.

• C1 = 30 + 10x and C2 = 20 + 5x; costs are the same when x = 3 classes.

A bookstore sells novels for $12 each and textbooks for $25 each. If they sold a total of 40 books and made $600, what system of equations can you create to find the number of novels and textbooks sold?

• x + y = 30, 12x + 20y = 600

• x + y = 50, 10x + 25y = 600

• x + y = 40, 15x + 20y = 600

• x + y = 40, 12x + 25y = 600

A gardener is planting flowers and shrubs. Each flower costs $3 and each shrub costs $5. If the gardener buys a total of 20 plants and spends $60, how can you represent this situation with a system of equations?

• x + y = 20, 3x + 5y = 60

• x + y = 15, 3x + 5y = 75

• x + y = 20, 2x + 4y = 60

• x + y = 25, 3x + 5y = 50