$\frac{x}{3}=\frac{16}{24}$

To solve the equation $\frac{x}{3} = \frac{16}{24}$, we first analyze the given expression. It is a linear equation with one unknown variable, $x$. The right-hand side is a fraction that can be simplified before we isolate $x$.

Simplifying the Equation

First, we simplify the fraction $\frac{16}{24}$. Both the numerator and the denominator are divisible by 8:
\[\frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}.\]
Now, our equation becomes:
\[\frac{x}{3} = \frac{2}{3}.\]

Solving for x

To isolate $x$, we multiply both sides of the equation by 3:
\[x = \frac{2}{3} \times 3.\]
This simplifies to:
\[x = 2.\]
Thus, the value of $x$ that satisfies the equation is 2.

Examples

Imagine you are mixing paint and need to maintain a specific ratio. If your recipe requires 1 part of a specific pigment for every 3 parts of base, but you only have a smaller container where you use 24 parts of base, you would need to calculate how many parts of pigment to use. Using the ratio $\frac{x}{3} = \frac{16}{24}$ is a practical way to ensure your mixture proportions remain consistent regardless of the total volume.