ESAT Maths 1 · free worked solution

ESAT Maths 1 formulae: make q the subject

Algebra solution: rearrange a fractional formula carefully to make q the subject.

Rearranging formulaeSpecification M4.7Reviewed 5 August 2026

Answer first

Option D

The correct answer is

q=Pr/(3−P)q = P r/(3 − P)

Clear the denominator first, then collect the terms containing q on one side.

This is original UniGenius practice material from the reviewed Maths 1 bank. It is not an official UAT-UK question, past paper, or recalled question.

The question

Read the setup, then choose the shortest valid route

For P≠3P ≠ 3, which expression makes qq the subject of P=3q/(q+r)P = 3q/(q + r)?

  • Aq=3Pr/(3−P)q = 3P r/(3 − P)
  • Bq=P/(3r−P)q = P/(3r − P)
  • Cq=r(3−P)/Pq = r(3 − P)/P
  • Dq=Pr/(3−P)q = P r/(3 − P)Answer
  • Eq=Pr/(P−3)q = P r/(P − 3)

Worked solution

The route in 4 steps

  1. Multiply both sides by q+r:P(q+r)=3qq + r: P(q + r) = 3q.

  2. Expand the left-hand side: Pq ++ Pr =3q= 3q.

  3. Move Pq to the right: Pr =3q−Pq=q(3−P)= 3q - P q = q(3 - P).

  4. Since P≠3P \ne 3, divide by 3−P3 - P to obtain q=Pr/(3−P)q = P r/(3 - P).

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