Let's solve the question "495 is 55 percent of what number?" step by step to identify the correct equation.
1. Understand the problem: We need to find the number [tex]\( x \)[/tex] such that 55% of [tex]\( x \)[/tex] equals 495.
2. Step-by-step solution:
- First, represent the unknown number as [tex]\( x \)[/tex].
- Set up the equation for the relationship given in the problem:
[tex]\[
0.55 \times x = 495
\][/tex]
- To isolate [tex]\( x \)[/tex], divide both sides of the equation by 0.55:
[tex]\[
x = \frac{495}{0.55}
\][/tex]
- Calculate the value of [tex]\( x \)[/tex] to get the answer.
Based on this step-by-step approach, we are looking for an equation that matches these steps. Let's examine the given options:
- [tex]\(\frac{55 \times 1}{495 \times 1}=\frac{55}{495}\)[/tex]: This option represents a fraction reduction and doesn't fit our problem context.
- [tex]\(\frac{100 \times 45}{55 \times 45}=\frac{4500}{2475}\)[/tex]: This equation simplifies a ratio, but it doesn't align with the equation [tex]\( x = \frac{495}{0.55} \)[/tex].
- [tex]\(\frac{45 \times 9}{100 \times 9}=\frac{405}{900}\)[/tex]: Similar to the above, this simplification does not fit our needed equation.
- [tex]\(\frac{55 \times 9}{100 \times 9}=\frac{495}{900}\)[/tex]: This is an exact fraction representation but not a proper direct representation of [tex]\( x = \frac{495}{0.55} \)[/tex].
The correct equation that aligns directly with the solution [tex]\( x = \frac{495}{0.55} \)[/tex] is:
[tex]\[
\frac{55 \times 9}{100 \times 9}=\frac{495}{900}
\][/tex]
This simplification retains the relationship implied by the given percentages and the resultant fraction equals the problem's requirement. The other equations do not correctly represent the necessary relationship.
Therefore, the most relevant equation, though not a perfect directive equation, is:
[tex]\[
\frac{55 \times 9}{100 \times 9}=\frac{495}{900}
\][/tex]
which aligns fairly with simplifying the problem correctly into the proportion context, ultimately leading towards isolating [tex]\( x = \frac{495}{0.55} \)[/tex].
