Question

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

3/16
3
16
units
Start Fraction 3 over 16 End Fraction units

6 units
6 units

0.5 units
0.5 units

1.5 units

Answer 1

To solve the equation \( \frac{x}{8} = \frac{y}{16} \) for \( x \) when \( y = 3 \), we can start by substituting \( y \) into the equation:

\[
\frac{x}{8} = \frac{3}{16}
\]

Next, we can cross-multiply to solve for \( x \):

\[
16x = 3 \cdot 8
\]

This simplifies to:

\[
16x = 24
\]

Now, divide both sides by 16:

\[
x = \frac{24}{16}
\]

Reducing the fraction gives:

\[
x = \frac{3}{2} = 1.5
\]

Thus, the value of \( x \) is **1.5 units**.