\frac{32 + x}{60} = \frac{66}{100} = \frac{33}{50}

["Solving the Equation: How to Solve $\frac{32 + x}{60} = \frac{66}{100} = \frac{33}{50}$", "Understanding how to solve equations involving fractions is essential in algebra, and this specific equation—$\frac{32 + x}{60} = \frac{66}{100} = \frac{33}{50}$—offers a clear example of solving for an unknown variable like $x$. In this guide, we’ll walk through the step-by-step process of simplifying and solving the equation, including why these two fractions are equal and how to find $x$.", "### Why Are the Fractions Equal?", "The equation starts with a statement that two fractions are equal:\n$$\n\frac{32 + x}{60} = \frac{66}{100} = \frac{33}{50}\n$$\nFirst, simplify $\frac{66}{100}$ and $\frac{33}{50}$:\n$$\n\frac{66}{100} = \frac{33 \ imes 2}{50 \ imes 2} = \frac{33}{50}\n$$\nSo, both fractions reduce to $\frac{33}{50}$. The equation is equivalent to:\n$$\n\frac{32 + x}{60} = \frac{33}{50}\n$$", "### Step-by-Step Solution", "#### Step 1: Eliminate the denominators\nTo solve for $x$, eliminate the denominators by cross-multiplying:\n$$\n(32 + x) \ imes 50 = 60 \ imes 33\n$$", "#### Step 2: Simplify both sides\nSimplify the right-hand side:\n$$\n60 \ imes 33 = 1,980\n$$\nNow the equation is:\n$$\n50(32 + x) = 1,980\n$$", "#### Step 3: Distribute and solve for $x$\nDistribute 50 across $32 + x$:\n$$\n50 \ imes 32 + 50x = 1,980\n\Rightarrow 1,600 + 50x = 1,980\n$$", "Subtract 1,600 from both sides:\n$$\n50x = 1,980 - 1,600 = 380\n$$", "Divide by 50:\n$$\nx = \frac{380}{50} = 7.6\n$$", "### Verifying the Solution", "Check that $x = 7.6$ satisfies the original equation:\n$$\n\frac{32 + 7.6}{60} = \frac{39.6}{60} = 0.66\n$$\nNow convert $\frac{33}{50}$:\n$$\n\frac{33}{50} = 0.66\n$$\nBoth sides match, confirming $x = 7.6$ is correct.", "### Why This Equation Matters", "Solving equations with fractions is fundamental in algebra, especially when modeling real-world problems involving rates, proportions, and percentages. Mastering these techniques builds a strong foundation for higher-level math, including geometry, trigonometry, and calculus.", "---", "### Summary", "- The equation $\frac{32 + x}{60} = \frac{66}{100}$ simplifies to $\frac{32 + x}{60} = \frac{33}{50}$.\n- Cross-multiplication removes denominators efficiently.\n- Solving step-by-step leads to $x = 7.6$.\n- Verification ensures accuracy.", "If you're learning algebra, practicing equations like this strengthens your ability to manipulate expressions and solve for unknowns. Continue practicing with different fractions and variables—mastery comes with repetition!", "---", "Keywords for SEO: \nsolve linear equations, algebra tutorial, solve for x, fractions equation, cross multiply, algebraic equations, fraction simplification, math problem solving, downloadable algebra exercises, beginner algebra guide", "---", "Related Search Terms:\n"How to solve (32 + x)/60 = 66/100", "solve variables in fractions", "step-by-step solving equations", "fractions simplification math homework"."]