Total: t + 3t = 4t = 64 → t = 64 ÷ 4 = 16

Understanding the Equation: How Calculating Total (4t) from t + 3t = 64 Helps Solve for t = 16

When faced with a simple algebraic equation like t + 3t = 64, many people wonder how they arrive at the solution — and how just dividing by 4 gives t = 16. This process is a foundational skill in algebra and plays a key role in solving real-world problems efficiently. In this article, we’ll break down the equation t + 3t = 64, explain why 4t = 64, and show how to find t by dividing both sides by 4.

Why Start with t + 3t = 64?

Understanding the Context

At first glance, the expression t + 3t might seem unclear. However, when simplified, it becomes straightforward:

t + 3t combines like terms, turning into (1 + 3)t = 4t.

So, t + 3t = 64 simplifies to:

4t = 64

Key Insights

This essential manipulation is where algebra becomes powerful — transforming complex-looking expressions into simpler forms that are easier to solve.

Solving for t by Dividing Both Sides by 4

Once simplified to 4t = 64, the next step is isolating the variable t. In algebra, the goal is to perform the same operation on both sides of the equation to maintain balance. Since t is multiplied by 4, reversing that multiplication requires division:

Divide both sides by 4:
4t ÷ 4 = 64 ÷ 4
This simplifies to:
t = 64 ÷ 4

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Final Thoughts

Performing the division gives:
t = 16

So, t = 16 is the correct solution.

Real-World Applications of This Concept

This type of equation appears in many practical scenarios:

Sales and revenue: If each product sells for t dollars and you sold 4 (1 + 3) units, totaling revenue of 64, the price per item is found by dividing total revenue by total units.
Time and work: If a task takes t hours and three similar tasks take 4t total hours, calculating t helps plan schedules.
Everyday budgeting: If a certain expense repeats and totals 64, and one part is t, dividing by the number of parts reveals the cost of one unit.

Summary: Key Takeaways

| Step | Action | Result |
|------|--------|--------|
| 1 | Combine like terms: t + 3t = 4t | 4t = 64 |
| 2 | Isolate t by dividing both sides by 4 | t = 64 ÷ 4 |
| 3 | Calculate | t = 16 |

Understanding how to simplify expressions and isolate variables is crucial for solving equations quickly and accurately. Remember: when you see 4t = 64, dividing by 4 gives t = 16 — a small adjustment that unlocks the full solution.

Whether you're a student learning algebra, a professional solving practical problems, or anyone tackling math in daily life, mastering this step-by-step approach simplifies complex thinking into clear, confident answers.