Solve $\frac{2}{3}=\frac{x}{18}$.
Answer (1)
We have the equation 3 2 = 18 x .
Multiply both sides by 18: 18 ⋅ 3 2 = x .
Simplify the left side: 3 36 = x .
Calculate the value of x : x = 12 , so the final answer is 12 .
Explanation
Understanding the Problem We are given the equation 3 2 = 18 x and asked to solve for x . This is a proportion problem, where we need to find the value of x that makes the two ratios equal.
Isolating x To solve for x , we can multiply both sides of the equation by 18 to isolate x on one side. This gives us: 18 ⋅ 3 2 = 18 ⋅ 18 x Simplifying, we get: 3 18 × 2 = x 3 36 = x
Calculating x Now, we perform the division: x = 3 36 = 12
Final Answer Therefore, the value of x that satisfies the equation is 12.
Examples
Imagine you are baking a cake and the recipe calls for 3 2 cup of sugar for every 18 servings. If you only want to make 12 servings, you can use the proportion 3 2 = 18 x to determine that you need 12 cups of sugar. Proportions are useful in scaling recipes, converting units, and many other real-life situations where you need to maintain a constant ratio.
