Let's solve the problem step-by-step:
1. We are given that [tex]\(90\% \)[/tex] of [tex]\(A\)[/tex] is equal to [tex]\(30\%\)[/tex] of [tex]\(B\)[/tex]. Mathematically, this can be written as:
[tex]\[
0.9A = 0.3B
\][/tex]
2. We need to find the value of [tex]\(x\)[/tex] such that [tex]\(B\)[/tex] is [tex]\(x\%\)[/tex] of [tex]\(A\)[/tex]. This can be written as:
[tex]\[
B = \frac{x}{100}A
\][/tex]
3. Let's use the given equality [tex]\(0.9A = 0.3B\)[/tex] and substitute the expression for [tex]\(B\)[/tex]:
[tex]\[
0.9A = 0.3 \left(\frac{x}{100}A \right)
\][/tex]
4. Simplify the equation by isolating [tex]\(x\)[/tex]. First, multiply both sides by 100 to avoid dealing with the fraction:
[tex]\[
90A = 0.3xA
\][/tex]
5. Next, we can divide both sides by [tex]\(A\)[/tex] (assuming [tex]\(A \neq 0\)[/tex]):
[tex]\[
90 = 0.3x
\][/tex]
6. Isolate [tex]\(x\)[/tex] by dividing both sides by 0.3:
[tex]\[
x = \frac{90}{0.3}
\][/tex]
7. Perform the division:
[tex]\[
x = 300
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{300}\)[/tex].
