To solve the given ratio and proportion problem, let's go through it step-by-step.
The given proportion is:
[tex]\[ 30 : 45 :: 5 : x \][/tex]
This notation means:
[tex]\[ \frac{30}{45} = \frac{5}{x} \][/tex]
To find [tex]\(x\)[/tex], we can use the property of proportions which states that the product of the means equals the product of the extremes. Therefore, we have:
[tex]\[ 30 \times x = 45 \times 5 \][/tex]
Now, let's solve for [tex]\(x\)[/tex]:
1. Multiply [tex]\(45\)[/tex] and [tex]\(5\)[/tex]:
[tex]\[ 45 \times 5 = 225 \][/tex]
2. Next, to find [tex]\(x\)[/tex], we divide [tex]\(225\)[/tex] by [tex]\(30\)[/tex]:
[tex]\[ x = \frac{225}{30} \][/tex]
3. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is [tex]\(15\)[/tex]:
[tex]\[ \frac{225 \div 15}{30 \div 15} = \frac{15}{2} = 7.5 \][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(7.5\)[/tex].
Therefore, the correct option is:
[tex]\[ a. \, x = 7.5 \][/tex]
