Exploring Linear Systems: Rate of Change in Real Life

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a system of equations to represent the total cost for renting a car for x miles. What is the rate of change in cost per mile?

• The rate of change in cost per mile is $0.50.

• The rate of change in cost per mile is $0.10.

• The rate of change in cost per mile is $0.30.

• The rate of change in cost per mile is $0.20.

A local bakery sells cupcakes for $2 each and cookies for $1.50 each. If a customer buys a total of 10 items for $17.50, write a system of equations to represent the situation. How many cupcakes and cookies did the customer buy?

• 6 cupcakes and 4 cookies

• 5 cupcakes and 5 cookies

• 4 cupcakes and 6 cookies

• 3 cupcakes and 7 cookies

A gym charges a monthly fee of $30 plus $5 for each class attended. If a member pays $70 in total, write a system of equations to find out how many classes they attended. What is the rate of change in cost per class?

• The member attended 10 classes and the rate of change in cost per class is $4.

• The member attended 8 classes and the rate of change in cost per class is $5.

• The member attended 5 classes and the rate of change in cost per class is $6.

• The member attended 3 classes and the rate of change in cost per class is $7.

A phone plan costs $40 per month plus $0.10 per text message. If a user spends $60 in a month, write a system of equations to determine how many text messages they sent. What is the rate of change in cost per text?

• 100

• 150

• 250

• 200

A school is selling tickets for a play. Adult tickets are $8 and student tickets are $5. If they sold a total of 100 tickets for $640, write a system of equations to find out how many adult and student tickets were sold. What does the solution represent?

• Adult tickets sold: 30, Student tickets sold: 70

• Adult tickets sold: 50, Student tickets sold: 50

• Adult tickets sold: 20, Student tickets sold: 80

• Adult tickets sold: 40, Student tickets sold: 60

A gardener is planting flowers in two types of pots. Pot A holds 5 flowers and Pot B holds 3 flowers. If the gardener has 30 flowers and wants to use all pots, write a system of equations to find out how many pots of each type are used. What is the rate of change in the number of flowers per pot?

• x + y = 30; Rate of change = 1 flower per pot

• x + y = 10; Rate of change = 3 flowers per pot

• x + y < 0; Rate of change = 5 flowers per pot

• x + y > 0; Rate of change = 2 flowers per pot

A bookstore sells novels for $12 and magazines for $5. If a customer buys a total of 15 items for $100, write a system of equations to find out how many novels and magazines were purchased. How does the solution relate to the total cost?

• 10 novels and 5 magazines

• 3 novels and 12 magazines

• 5 novels and 10 magazines

• 7 novels and 8 magazines

A taxi company charges a base fare of $3 plus $2 per mile. If a passenger pays $15 for a ride, write a system of equations to find out how many miles they traveled. What does the slope indicate about the cost per mile?

• 6 miles

• 10 miles

• 8 miles

• 4 miles

A factory produces two types of toys. Toy A costs $4 to make and Toy B costs $6. If the factory spends $240 to produce a total of 50 toys, write a system of equations to find out how many of each type were produced. What does the solution signify in terms of production costs?

• Toy A: 25, Toy B: 25

• Toy A: 30, Toy B: 20

• Toy A: 40, Toy B: 10

• Toy A: 20, Toy B: 30