DEPENDENT AND INDEPENDENT VARIABLES WORD PROBLEMS

Problem 1 :

Mary can make 5 hairbows every hour. Which is the independent variable?

a. Number of hours Mary makes bows

b. Number of hairbows made per hour

c. Total number of hairbows that Mary made

d. Price of each hairbow

Solution :

Mary can make 5 hairbows for an hour. For 2 hours, she can make 10 hair bows.

So, the number of hours she is working is independent. Then option a is correct.

Problem 2 :

The formula for the circumference of a circle is

C = πd

where C is the circumference and d is the diameter. Identify the dependent variable.

Solution :

Here diameter (d) is the independent variable and C is the dependent variable.

Problem 3 :

Select all of the scenarios below that correctly identify the independent variable.

a. Charlie gets paid by the hour. The number of hours he works is the independent variable.

b. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.

c. How much Caleb weighs is relative to the amount he eats. The amount he weighs is the independent variable.

d. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.

Solution :

Scenario a :

The number of hours is independent and payment is dependent.

Scenario b :

The distance covered is independent and cost of the trip is dependent.

Scenario c :

The amount he eats is independent but in the given scenario says weight is independent. So, it is incorrect.

Scenario d :

The amount of time he is taking to practice is independent. IT is true.

So, Scenarios a, b and d are correct.

Problem 4 :

What is the dependent variable in the following equation?

y = 3x + 9

a. x       b. 3       c. 9         d. y

Solution :

Here based on the value of x that we apply, we will receive the value of y. So, x is independent and y is dependent. Then the answer is d.

Problem 5 :

Which is the independent variable in the following equation?

y = 3x + 9

a. x      b. 3       c. 9      d. y

Solution :

x is the independent variable.

Problem 6 :

Your car can travel 17 miles on a gallon of gas. Which is the independent variable?

a. Total number of miles you travel

b. Number of gallons of gas you have in the tank

c. Number of miles you travel on a gallon of gas

d. Total number of hours you travel 

Solution :

Using one gallon of gas, we can travel 17 miles. Here the number of number of gallons of gas in the tank is independent and number of miles you travel is dependent. So, option b is correct.

Problem 7 :

As a babysitter, you earn $5 for every hour you babysit. Which is the dependent variable?

a. Amount of money you earn per hour

b. Number of hours you babysit

c. Total amount of money you earn

d. Number of children you babysit

Solution :

For every hours that you baby sit will be the independent variable. The amount that you earn is the dependent variable. 

So, option c is correct.