Solve: [tex]\frac{u}{u-4}=\frac{24}{17}[/tex].
Answer (2)
Cross-multiply the equation: 17 u = 24 ( u − 4 ) .
Distribute on the right side: 17 u = 24 u − 96 .
Isolate u terms: 7 u = 96 .
Solve for u : u = 7 96 .
7 96
Explanation
Problem Setup We are given the equation u − 4 u = 17 24 and we want to solve for u .
Cross-Multiplication To solve this equation, we can cross-multiply to eliminate the fractions. This gives us: 17 u = 24 ( u − 4 ) .
Distribution Next, we distribute the 24 on the right side of the equation: 17 u = 24 u − 24 × 4 17 u = 24 u − 96
Isolating u Terms Now, we want to isolate the u terms. We can subtract 17 u from both sides: 0 = 24 u − 17 u − 96 0 = 7 u − 96
Adding 96 to Both Sides Add 96 to both sides: 96 = 7 u
Solving for u Finally, we divide both sides by 7 to solve for u : u = 7 96
Final Answer Therefore, the solution to the equation is u = 7 96 .
Examples
Imagine you're scaling a recipe. The ratio of ingredients needs to stay the same. This problem is similar; it helps maintain the correct proportions when one part of the ratio changes. Understanding how to solve such equations is crucial in fields like cooking, chemistry, and engineering, where maintaining precise ratios is essential for desired outcomes. This skill ensures that when you adjust one variable, you can accurately adjust others to keep everything in balance.
To solve the equation u − 4 u = 17 24 , we cross-multiply to get 17 u = 24 ( u − 4 ) . Then, by isolating the variable u , we find that u = 7 96 .
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