To solve the ratio [tex]\( \frac{2}{6} = \frac{X}{10} \)[/tex] for [tex]\( X \)[/tex], let's go through the problem step-by-step:
1. Understand the given ratio: The problem presents the ratio [tex]\(\frac{2}{6}\)[/tex] and equates it to [tex]\(\frac{X}{10}\)[/tex].
2. Set up the equation: Given [tex]\(\frac{2}{6} = \frac{X}{10}\)[/tex], we need to find the value of [tex]\( X \)[/tex] that makes this equation true.
3. Cross-multiply to solve for [tex]\( X \)[/tex]: To eliminate the fractions, we can cross-multiply. This means we will multiply the numerator of the first fraction by the denominator of the second fraction and equate it to the product of the denominator of the first fraction and the numerator of the second fraction:
[tex]\[
2 \cdot 10 = 6 \cdot X
\][/tex]
4. Simplify the equation: Now, multiply the numbers:
[tex]\[
20 = 6X
\][/tex]
5. Solve for [tex]\( X \)[/tex]: Now, we need to isolate [tex]\( X \)[/tex] by dividing both sides of the equation by 6:
[tex]\[
X = \frac{20}{6}
\][/tex]
6. Simplify the result: Simplify the fraction [tex]\(\frac{20}{6}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
X = \frac{20 \div 2}{6 \div 2} = \frac{10}{3}
\][/tex]
7. Convert to decimal form (if needed): Dividing 10 by 3 gives:
[tex]\[
X = 3.3333333333333335
\][/tex]
Thus, the value of [tex]\( X \)[/tex] that satisfies the ratio [tex]\(\frac{2}{6} = \frac{X}{10}\)[/tex] is approximately [tex]\( X = 3.3333333333333335 \)[/tex].
