Total salt: 0.25x + 0.10(300 - x) = 0.15 × 300. - Deep Underground Poetry
Total Salt Explained: Solving the Equation 0.25x + 0.10(300 - x) = 0.15 × 300
Total Salt Explained: Solving the Equation 0.25x + 0.10(300 - x) = 0.15 × 300
Understanding vital nutritional concepts starts with mastering basic algebra—and sometimes, that involves solving equations that model real-world scenarios. One practical example comes from calculating total salt content in food preparation, where balancing salt intake is essential for health.
The Equation Breakdown: Total Salt Formula
Understanding the Context
We’re given the equation:
0.25x + 0.10(300 - x) = 0.15 × 300
Let’s break this down step-by-step for clarity.
What Does Each Term Represent?
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Key Insights
- x: Represents the amount (in grams or similar units) of a solution with 25% salt concentration.
- 0.25x: The total salt in x grams of this 25% salt solution.
- (300 - x): The remaining amount — 300 grams minus x — of a solution with 10% salt concentration.
- 0.10(300 - x): Salt content from (300 - x) grams of the 10% solution.
- 0.15 × 300: This is the total target salt amount: 15% of 300 grams = 45 grams.
Solving the Equation: Step-by-Step
Start with:
0.25x + 0.10(300 - x) = 45
Distribute the 0.10:
0.25x + 30 - 0.10x = 45
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Combine like terms:
(0.25 - 0.10)x + 30 = 45
0.15x + 30 = 45
Subtract 30 from both sides:
0.15x = 15
Divide both sides by 0.15:
x = 15 ÷ 0.15 = 100
Interpretation: What Does x = 100 Mean?
- x = 100 grams is the amount of the 25% salt solution.
- That means 300 - x = 200 grams of a 10% salt solution is mixed.
- The total salt content equals 45 grams, achieving a helpful 15% salt concentration in the combined 300-gram mixture.
Practical Application
This formula simplifies calculating salt content in mixed solutions—useful in culinary math, nutrition planning, or food label analysis. By solving such equations, dieticians, chefs, and home cooks ensure balanced salt intake, supporting heart health and dietary goals.
