Solve [tex]\frac{m+1}{2 m+1}=\frac{3}{5}[/tex]
Answer (1)
To solve the equation 2 m + 1 m + 1 = 5 3 :
Cross-multiply: 5 ( m + 1 ) = 3 ( 2 m + 1 ) .
Distribute: 5 m + 5 = 6 m + 3 .
Isolate m : 5 = m + 3 .
Solve for m : m = 2 .
The solution is 2 .
Explanation
Problem Analysis We are given the equation 2 m + 1 m + 1 = 5 3 . Our goal is to solve for m .
Cross-Multiplication To solve the equation, we can cross-multiply to eliminate the fractions. This gives us: 5 ( m + 1 ) = 3 ( 2 m + 1 ) .
Distribution Next, we distribute the constants on both sides of the equation: 5 m + 5 = 6 m + 3 .
Isolating m Now, we want to isolate m on one side of the equation. We can subtract 5 m from both sides: 5 = m + 3 .
Solving for m Finally, we subtract 3 from both sides to solve for m : m = 5 − 3 = 2 .
Final Answer Therefore, the solution to the equation is m = 2 .
Examples
Imagine you're scaling a recipe. The original recipe calls for a certain ratio of ingredients, say flour to water. If you want to make a larger batch while maintaining the same taste, you need to keep the ratio constant. This problem is similar to solving for the unknown amount of one ingredient when you know the desired ratio and the amount of the other ingredient. Understanding how to solve such equations ensures your scaled recipe turns out just right, with the flavors perfectly balanced.
