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b) [tex]\[ 4: \frac{2}{8} = \frac{\square}{3} \][/tex]

Sagot :

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]
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