Identifying Independent and Dependent Variables | Interactive ... - Free Printable

Let's solve each problem by identifying the independent variable and the dependent variable.

🔍 Key Concept:

- Independent Variable (IV): The variable that is changed or controlled in an experiment or situation.
- Dependent Variable (DV): The variable that responds to the change; it depends on the independent variable.

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✔ Problem 1:

The number of students in a class, s, and the number of desks needed, d

- Independent variable: s (number of students)
→ We decide how many students are in the class.
- Dependent variable: d (number of desks needed)
→ The number of desks depends on how many students there are.

✔ Answer:
- Independent variable: s
- Dependent variable: d

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✔ Problem 2:

The number of candles on a birthday cake, c, and the person’s age, a

- Independent variable: a (person’s age)
→ Age determines how many candles are placed.
- Dependent variable: c (number of candles)
→ Candles depend on the age.

✔ Answer:
- Independent variable: a
- Dependent variable: c

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✔ Problem 3:

The height of a sunflower in inches, h, and the number of days since it was planted, d

- Independent variable: d (number of days)
→ Time passes independently.
- Dependent variable: h (height)
→ Height grows as days pass.

✔ Answer:
- Independent variable: d
- Dependent variable: h

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✔ Problem 4:

The number of gallons of paint needed, g, and the area of a room in square feet, a

- Independent variable: a (area of the room)
→ The size of the room is given first.
- Dependent variable: g (gallons of paint)
→ Paint needed depends on the area.

✔ Answer:
- Independent variable: a
- Dependent variable: g

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✔ Problem 5:

The number of eggs Dorina has, e, and the number of batches of muffins she can bake, b

- Independent variable: e (number of eggs)
→ She starts with a certain number of eggs.
- Dependent variable: b (batches of muffins)
→ How many batches she can make depends on how many eggs she has.

✔ Answer:
- Independent variable: e
- Dependent variable: b

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✔ Problem 6:

The amount of money Isabella earns, m, and the number of hours she works, h

- Independent variable: h (hours worked)
→ She chooses how many hours to work.
- Dependent variable: m (money earned)
→ Earnings depend on hours worked.

✔ Answer:
- Independent variable: h
- Dependent variable: m

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✔ Problem 7:

The number of T-shirts a basketball team orders, t, and the number of players on the team, p

- Independent variable: p (number of players)
→ The team size determines how many shirts are needed.
- Dependent variable: t (number of T-shirts)
→ Number of shirts depends on the number of players.

✔ Answer:
- Independent variable: p
- Dependent variable: t

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✔ Problem 8:

The number of miles Terrence has driven, m, and the amount of gas he has used, g

- Independent variable: m (miles driven)
→ Distance traveled is what we measure first.
- Dependent variable: g (gas used)
→ Gas consumption depends on how far he drives.

✔ Answer:
- Independent variable: m
- Dependent variable: g

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📝 Final Answers Summary:

| Problem | Independent Variable | Dependent Variable |
|--------|----------------------|--------------------|
| 1 | s | d |
| 2 | a | c |
| 3 | d | h |
| 4 | a | g |
| 5 | e | b |
| 6 | h | m |
| 7 | p | t |
| 8 | m | g |

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💡 Tip: Ask yourself: "Which one causes the change?" The cause is the independent variable. The effect is the dependent variable.

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