Make \(q\) the subject of the formula: \(\frac{q-r}{t} = \frac{v-q}{v}\)
A. \(q = \frac{v(t+r)}{v+t}\)
B. \(q = \frac{vt+r}{t-v}\)
C. \(q = r(\frac{v-t}{v})\)
D. \(q = \frac{v-q}{v} + \frac{r}{t}\)
Correct Answer: A
Explanation
To make \( q \) the subject of the formula in the equation \(\frac{q-r}{t} = \frac{v-q}{v}\), we will follow these steps:
Step-by-Step Solution:
1. Cross multiply to eliminate the fractions:
\[
v(q - r) = t(v - q)
\]
2. **Expand both sides:**
\[
vq - vr = tv - tq
\]
3. Collect all terms involving \( q \) on one side of the equation:
\[
vq + tq = tv + vr
\]
Combine like terms:
\[
q(v + t) = vr + tv
\]
4. Solve for \( q \):
\[
q = \frac{vr + tv}{v + t}
\]
Factor out the common terms in the numerator:
\[
q = \frac{v(t + r)}{v + t}
\]
The correct answer is A - \( q = \frac{v(t+r)}{v+t} \)
