Ethan writes the ratio x/8 = y/16 to help him reduce the size of a two-dimensional shape. If the new value of y is 3 units, what will be the value of x?

Answer 1

To find the value of $x$ given the ratio $\frac{x}{8}=\frac{y}{16}$ and $y=3$, we start by substituting $y$ into the equation:

$$\frac{x}{8}=\frac{3}{16}$$

Next, we can solve for $x$ by cross-multiplying:

$$x\cdot 16=3\cdot 8$$

Calculating $3\cdot 8$:

$$3\cdot 8=24$$

So we have:

$$16x=24$$

Now, divide both sides by 16 to isolate $x$:

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

Now simplify $\frac{24}{16}$:

$$x=\frac{24÷8}{16÷8}=\frac{3}{2}$$

Thus, the value of $x$ is

$$\boxed{{\displaystyle \frac{3}{2}}}$$