y / (x / p * 100) * 100 = q ; solve for q

To solve for \( q \) in the equation:

\[
\frac{y}{\left(\frac{x}{p} \times 100\right)} \times 100 = q
\]

we can simplify the equation step-by-step.

1. Simplify the term inside the denominator:

\[
\frac{x}{p} \times 100 = \frac{100x}{p}
\]

So, the equation becomes:

\[
\frac{y}{\frac{100x}{p}} \times 100 = q
\]

2. Simplify the fraction by multiplying \( y \) by the reciprocal of \( \frac{100x}{p} \):

\[
\frac{y \times p}{100x} \times 100 = q
\]

3. Multiply by \( 100 \):

\[
\frac{yp}{x} = q
\]

Hence, the solution for \( q \) is:

\[
q = \frac{yp}{x}
\]

Do you want more details or have any questions?

Here are 5 related questions for further exploration:
1. What would be the value of \( q \) if \( y = 50 \), \( x = 10 \), and \( p = 2 \)?
2. How does the equation change if \( p \) is doubled?
3. What is the interpretation of \( q \) in this context?
4. How would you isolate \( y \) in the original equation?
5. What would happen to \( q \) if both \( x \) and \( y \) are increased by a factor of 10?

**Tip:** When simplifying complex fractions, multiplying by the reciprocal of the denominator can often make the problem much easier to handle.

Learn how to solve the rational equation y / (x / p * 100) * 100 = q. This step-by-step solution simplifies complex fractions and applies reciprocal multiplication, resulting in the formula q = (yp) / x. Suitable for students in Grades 9-11.

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