3n + 4p = 7.80 \quad \text(1) - Parker Core Knowledge
Understanding the Linear Equation: 3n + 4p = 7.80
Understanding the Linear Equation: 3n + 4p = 7.80
When solving equations like 3n + 4p = 7.80, we dive into the foundational world of algebra, unlocking the relationship between two variables — typically representing cost, quantity, or rate. This equation serves as a powerful model in various real-world contexts such as economics, budgeting, and business pricing.
Understanding the Context
What Is the Equation 3n + 4p = 7.80?
The equation 3n + 4p = 7.80 is a linear Diophantine expression involving two variables:
- n often represents the quantity of one item, such as a unit of product A, priced at $3 per unit.
- p stands for the quantity of another item, say product B, at $4 per unit.
The right-hand side, 7.80, is the total cost — the sum of costs from buying n units of product A and p units of product B.
Image Gallery
Key Insights
In short:
Total cost = (price per unit × quantity) for both products = $7.80
Solving for One Variable
To make sense of this equation, solving for one variable in terms of the other clarifies relationships within the system.
Solving for p:
Start from equation (1):
3n + 4p = 7.80
🔗 Related Articles You Might Like:
📰 First, assume the initial ice cover is 100%. After losing 12%, 88% remains. 📰 Total ice lost = 12% + 13.2% = 25.2%. 📰 Therefore, 25.2% of the original ice cover was lost. 📰 Downloads Games Free 7666668 📰 You Wont Believe How Addictive This App Game Isplay Now 2684633 📰 You Wont Believe What Happened In Tb Daily News This Week Shocking Updates 1122845 📰 3 Unlock The Applicazione Wish Apk With This Still Sneaky Method 6888543 📰 These 7 Angelic Lyrics Will Make You Start Talking To Angels Tooyou Wont Believe How Powerful They Are 8637237 📰 Secrets Of The Mens Barbers That Changes Faces Forever 9857000 📰 The Final Showdown That Refused To Enducla Vs Usc Rivalry Live Again 1824086 📰 Khadija 2806148 📰 Walt Disney World En Orlando 3573678 📰 Bank Of America Routing Number San Francisco 3812208 📰 53 Maybe Its Madden New Release Date Sparks Wild Excitement In The Gaming World 469313 📰 Mtc Stock Shock Investors Are Reacting After This Massive Breakthrough 3247747 📰 Is This The Most Stunning Pearl Abyss Discovery Of The Decade Find Out Now 8256411 📰 Waveful Hacks You Wont Believe Are Changing How We Experience Digital Trends 5787176 📰 The Shock Begins Everything You Missed About Gme Eps Exploded Tonight 4121651Final Thoughts
Subtract 3n from both sides:
4p = 7.80 – 3n
Then divide both sides by 4:
p = (7.80 – 3n) / 4
This formula lets you compute the value of p for any given n, as long as the result is a non-negative real number if quantities must be non-negative.
Practical Applications
-
Budgeting and Shopping
Imagine buying oranges (n) at $3 per kg and apples (p) at $4 per kg. With a fixed budget of $7.80, this equation helps determine how many of each fruit you can buy. -
Cost Analysis in Business
In manufacturing, the equation models total production costs based on units of two raw materials or labor tiers.
- Market Equilibrium Studies
Social scientists and economists use similar equations to model supply-demand scenarios where two variables influence a known total cost or revenue.
Finding Integer Solutions
For real-life scenarios where only whole units can be purchased, 3n + 4p = 7.80 poses a special challenge — full solutions in integers (wholesale buying, inventory units) rather than decimals.
