To solve the problem "495 is 55 percent of what number?", we can set up the equation based on the equation that 55% of some number (let's call it \(x\)) equals 495. This can be expressed mathematically as:
\[ 0.55 \times x = 495 \]
To solve for \(x\), we can rearrange the equation:
\[ x = \frac{495}{0.55} \]
Now, let's rewrite 0.55 as \( \frac{55}{100} \):
\[ x = \frac{495}{\frac{55}{100}} \]
When we divide by a fraction, it is equivalent to multiplying by its reciprocal:
\[ x = 495 \times \frac{100}{55} \]
We want to find an equation among the options provided that represents this.
Let's analyze the choices one by one:
A. \(\frac{55 \times 1}{495 \times 1} = \frac{55}{495}\) - This does not relate to our original equation.
B. \(\frac{100 \times 45}{55 \times 45} = \frac{4500}{2475}\) - This also does not hold.
C. \(\frac{45 \times 9}{100 \times 9} = \frac{405}{900}\) - This does not connect to our problem.
D. \(\frac{55 \times 9}{100 \times 9} = \frac{495}{900}\) - This simplifies down to \(\frac{55}{100} = \frac{495}{x}\), which is related to the original problem.
Therefore, the most applicable equation to solve for how 495 is 55 percent of a number is:
D. \(\frac{55 \times 9}{100 \times 9} = \frac{495}{900}\).
5 answers