0.05x + 0.08(10,000 - x) = 680 - Dyverse
Understanding the Equation: Solving 0.05x + 0.08(10,000 - x) = 680
Understanding the Equation: Solving 0.05x + 0.08(10,000 - x) = 680
When faced with a linear equation like 0.05x + 0.08(10,000 - x) = 680, it might seem daunting at first—but breaking it down step by step makes solving it straightforward. Whether you're a student learning algebra or a professional working through real-world financial calculations, understanding how to solve equations systematically is essential.
Understanding the Context
What is the Equation?
The equation 0.05x + 0.08(10,000 - x) = 680 models a weighted average scenario, commonly used in finance, cost analysis, or profit modeling. It balances two different rates applied to parts of a total quantity.
In this case:
- 0.05x represents 5% of a quantity x
- 0.08(10,000 - x) represents 8% applied to the remaining (10,000 - x)
Their sum equals 680, likely modeling a total weighted cost or return.
Image Gallery
Key Insights
Step 1: Expand the Expression
Start by distributing 0.08 across the parenthesis:
\[
0.05x + 0.08 \ imes 10,000 - 0.08x = 680
\]
Calculate \(0.08 \ imes 10,000 = 800\), so the equation becomes:
🔗 Related Articles You Might Like:
📰 The Secret Names Speakers Whisper at Midnight—Without a Word 📰 The Worst Witch Names Ever Conjured, Will You Recognize Yours? 📰 You’ll Never Guess These Work Shoes Transform Every Step You Take 📰 Step Into Elegance The Most Stylish Lace Corset Top Thats Taking Over Instagram 📰 Step Into Fire The Surprising Power Behind The Iconic Koudelka Gear 📰 Step Into Forgotten Land With Kirby The Shocking Truth Behind The Legend 📰 Step Into Hogwarts With This Epic Lego Harry Potter Set Show Us Your Creations 📰 Step Into Kirby Dreamland The Ultimate Dreamlike Adventure Awaits 📰 Step Into Lanvins Glamdiscover How These Slides Are Taking Runway Fashion By Storm 📰 Step Into Legacy Why Every Fan Needs A Kobe Basketball Jersey Now 📰 Step Into Lego Horizon Adventures Epic Builds That Will Blow Your Mind 📰 Step Into Luxury Lanvin Curb Sneakers That Wont Break The Bank 📰 Step Into Style Leopard Print Shoes Thatll Steal Every Look They Touch 📰 Step Into Style Light Blue Heels That Turn Heads Dont Miss Out 📰 Step Into Style Light Brown And Chic Accents That Boost Your Homes Appeal 📰 Step Into Style With The Ultimate Lamelo Ball Jerseystrendsetter Alert Inside 📰 Step Into The Dragon Ball Z Launchunlock The Power Of A Legend 📰 Step Into The Fast Lane Lightning Mcqueens Costume Leaves Everyone SpeechlessFinal Thoughts
\[
0.05x + 800 - 0.08x = 680
\]
Step 2: Combine Like Terms
Combine the x terms:
\[
(0.05 - 0.08)x + 800 = 680 \
-0.03x + 800 = 680
\]
Step 3: Isolate the Variable
Subtract 800 from both sides:
\[
-0.03x = 680 - 800 \
-0.03x = -120
\]
Now divide both sides by \(-0.03\):
