Make Q the subject of formula if p = $\frac{M}{5}$(X + Q) + 1

Analyze the question: We need to rearrange p = (M/5)(X + Q) + 1 so that Q stands alone on one side.

Concept: Use inverse operations. Undo the addition, then the multiplication and division, then the remaining addition.

Solution:

1. Start with the formula: p = (M/5)(X + Q) + 1

2. Subtract 1 from both sides: p − 1 = (M/5)(X + Q)

3. Multiply both sides by 5: 5(p − 1) = M(X + Q) 5p − 5 = MX + MQ

4. Subtract MX from both sides: 5p − 5 − MX = MQ

5. Divide both sides by M: Q = (5p − MX − 5)/M

Matching the options: This is (5P − MX − 5)/M, which is option B.

Check with numbers: Let M = 5, X = 1, Q = 2. Then p = (5/5)(1 + 2) + 1 = 4. Substituting into option B gives (20 − 5 − 5)/5 = 10/5 = 2. This matches Q, so the answer is correct.

Exam tip: When a formula has a fraction, clear it early by multiplying through by the denominator. Remember that "−1" must also be multiplied by 5, which gives −5. Many students lose marks by forgetting this step, and that mistake is what makes options A and C tempting. You can also confirm your answer quickly by substituting simple numbers, as we did above.