Sure, let's solve the given problem step-by-step.
We start with the given ratio:
[tex]\[ \frac{2}{8} = \frac{\square}{3-y} \][/tex]
We need to find the missing term (denoted by [tex]\(\square\)[/tex]) in this ratio. Let's denote the missing term by [tex]\(x\)[/tex]. Therefore, we rewrite the ratio as:
[tex]\[ \frac{2}{8} = \frac{x}{3-y} \][/tex]
To solve for [tex]\(x\)[/tex], we can cross-multiply:
[tex]\[ 2 \cdot (3 - y) = 8 \cdot x \][/tex]
This gives us the equation:
[tex]\[ 6 - 2y = 8x \][/tex]
Next, we solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{6 - 2y}{8} \][/tex]
Next, we make a simple assumption for [tex]\(y\)[/tex] to simplify our calculations. Let's assume [tex]\(y = 1\)[/tex]:
[tex]\[ x = \frac{6 - 2 \cdot 1}{8} \][/tex]
This simplifies to:
[tex]\[ x = \frac{6 - 2}{8} \][/tex]
[tex]\[ x = \frac{4}{8} \][/tex]
[tex]\[ x = 0.5 \][/tex]
Therefore, the missing term in the ratio is [tex]\(0.5\)[/tex]. So, the completed ratio is:
[tex]\[ \frac{4}{\frac{2}{8}} = \frac{0.5}{3-1} \][/tex]
Note that since [tex]\(y = 1\)[/tex], we update the denominator [tex]\(3-1\)[/tex] to [tex]\(2\)[/tex]. However, the problem stated the ratio before substitution:
Hence, the missing term [tex]\(\square\)[/tex] is:
[tex]\[ \boxed{0.5} \][/tex]
