Total: t + 3t = 4t = 64 → t = 64 ÷ 4 = 16 - Richter Guitar
Understanding the Equation: How Calculating Total (4t) from t + 3t = 64 Helps Solve for t = 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
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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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- 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.
