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If (P(t)=38+6t) and (Q(t)=122-8t), at which (t) will (P(t)=Q(t))?

Answer and explanation

Correct answer: \(t=6\)

For equality, set the two expressions equal: \(38+6t=122-8t\). Bringing \(8t\) to the left gives \(14t=84\), so \(t=6\). Although \(t=8\) is a close distractor, \(P(8)=86\) and \(Q(8)=58\), so they are not equal. Exam tip: when one expression increases and the other decreases, equate them to find their intersection time.

Related tags

Linear EquationsPolynomialsGrowth And DecayEquality Of ExpressionsAlgebraic SolvingLinear Growth And DecayIntroduction To PolynomialsMathematics

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