Total: t + 3t = 4t = 64 → t = 64 ÷ 4 = 16 - Redraw
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
Image Gallery
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
🔗 Related Articles You Might Like:
📰 katharina mazepa 📰 rick harrison pawn stars 📰 demi moore met gala 📰 Orche 8510878 📰 Lamelo Ball Fan Favorite Alert High Quality Jerseys That Slay On The Court 7686543 📰 No Tools No Problem Just The Ultimate Bottle Opener Secret 128844 📰 Your Free Parking Breakthrough The Secret Location No One Discusses 8578967 📰 Mvis News Breaks The Hidden Agenda No One Wants You To Know 8749109 📰 Front General Store Makeover Gallery Youll Wish You Came In Earlier 5656491 📰 France Traduction Anglais 5254037 📰 Egg Shockers 1945722 📰 Fire Returns With Inferno Power As Countrys Next Unstoppable Season Unfolds 5939904 📰 Frances Sme Financing Explosion Shocking News You Cant Ignore In 2024 1103789 📰 Orwell Nineteen Eighty Four 6076516 📰 1V1 Lol Chaos Watch Top Players Turn The Game Upside Down 703227 📰 Ready To Skyrocket Your Efficiency Discover How Outlook Power Automate Works 8188218 📰 When Does Wrestlemania Kick Off The Shocking Start Time That Affects Millions 4393426 📰 Boost Your Macbook Experience Download Spotify Tracks Offline Now 2715354Final 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.
