0.05x + 0.08(10,000 - x) = 680 - inBeat
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:
📰 How Much Is 2000 Vbucks 📰 Arknights Endfield Pc 📰 Computer Play 📰 Ghost In The Shell 2017 816520 📰 Mortal Kombat Movies That Shock Every Fanheres The Truth Coming To Your Screen 9597595 📰 How To Change Your Password In Steam 1398009 📰 You Wont Believe How Ave Christus Rex Church Shocked The Entire Diocesewhats Hidden In His Name 9139636 📰 Pdiddy 2400767 📰 Play With Your Bff 2 Player Multiplayer Games That Dominate Search 6856688 📰 Abcya Games Abcya Vs The Competition Why Kids Cant Get Enough 7344743 📰 Zenoti App Leak The Must Have Tool Thats Changing How You Stay Fit Forever 6467881 📰 This One Digital Tool Is Taking Over Your World In Ways You Never Imagined 4497315 📰 Farm Merge Valley Is Revolutionizing Agriculture Gamesplay This Mass 6735913 📰 Free Java Runtime Download Everything You Need To Get Jre Fast 5358251 📰 Saint Malo 1538740 📰 Whatsapp On The Mac 9535854 📰 Believed Synonym 9691076 📰 The King And I Movie 1956 7870562Final 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 \(-0.03\):
