IDENTIFY THE DEPENDENT AND INDEPENDENT VARIABLES 

Label each of the variables as independent or dependent variables.

Problem 1 :

Tamara's daughter is a dancer who will be participating in an upcoming recital. For each dance her daughter plans to perform, she will require a different costume.

Solution :

independent d = the number of dances Tamara's daughter plans to perform

dependent c = the number of costumes Tamara's daughter will require

Problem 2 :

Yardena is planning her wedding. The number of announcements she orders is determined by the number of guests she wants to invite.

Solution :

independent g = the number of guests

dependent a = the number of announcements

Problem 3 :

Spencer goes biking every morning. The farther he bikes, the more calories he burns during the bike ride.

Solution :

Dependent c = the number of calories Spencer burns during the bike ride

Independent d = the distance Spencer bikes

Problem 4 :

A committee is organizing a music festival in Jefferson County. The amount of time that the venue has been reserved for determines the number of bands that will be able to play at the festival.

Solution :

independent t = the amount of time that the venue has been reserved for

dependent b = the number of bands that will be able to play

Problem 5 :

Carson is selling lemonade. The number of cups of lemonade he sells determines how much money he earns.

Solution :

dependent m = the amount of money Carson earns

independent c = the number of cups of lemonade Carson sells

Problem 6 :

During the winter, a trucking company ships produce from California to Cleveland. The more produce the company needs to ship, the more truckers it will hire.

Solution :

dependent t = the number of truckers the company will hire

independent p = the amount of produce the company needs to ship

identify the independent and dependent variables in the given situation, graph the data on the coordinate plane and label the axes appropriately.

Problem 7 :

A florist wants to see if the amount of Product X will extend the life of cut flowers so that they last longer.

Independent – 

Dependent –

Solution:

Independent – Amount of product X

Dependent – life of cut flowers

Problem 8 :

A drug company wants to prevent sneezing for people with grass allergies. They test different doses of their new drug.

Independent – 

Dependent –

Solution:

Independent – Dose of medicine

Dependent – Number of sneezes

Read the situation, write an equation to represent the situation and solve the equation for the independent variable.

Problem 9 :

The Mayfield Drama Club is having a three day performance of Tarzan. If the tickets are free they will give away 750 tickets. The math department calculates that for every $1 increase in the cost of a ticket price that 23 less tickets are sold.

a. Using n to represent the number of ticket sold and c to represent the cost of a ticket, identify the independent and dependent variables.

b. Write an equation to represent this situation. Remember, equations usually start with the dependent variable!

c. Solve the equation for the independent variable.

d. If 566 tickets are sold, then what was the ticket price?

Solution:

a. 

n is dependent and c is independent

b.

n = 750 - 23c

c.

n - 750 = -23c

c = (750 - n)/23

d.

c = (750 - 566)/23

c = 184/23

c = 8 per ticket

Problem 10 :

There is a glacier located in Math Valley and it began melting due to global warming. The front of the glacier began at an elevation of 125 feet. The glacier moves up the valley at a rate of 2.25 feet per day.

a. Using E to represent the glacier’s current elevation and d to represent the number of days since the melting began, identify the independent and dependent variables.

b. Write an equation to represent this situation. 

c. Solve the equation for the independent variable.

d. If the glacier is at an elevation of 149.75 feet, how days have passed since the melting began?

Solution:

a. 

E is dependent and d is independent

b. 

E = 125 + 2.25d

c.

E - 125 = 2.25d

d = (E - 125)/2.25

d.

d = (149.75 - 125)/2.25

d = 24.75/2.25

d = 11 days