If (C(t)=130-5t) and (D(t)=70+3t), at what (t) will (C(t)) be (12) less than (D(t))?
Answer and explanation
Correct answer: \(t=9\)
“\(C(t)\) is 12 less than \(D(t)\)” means \(C(t)=D(t)-12\). Thus, \(130-5t=70+3t-12\). Simplifying gives \(72=8t\), so \(t=9\). Option \(t=8\) is close, but the difference between the two values is not 12 there. Exam tip: For “less than” comparisons, subtract the stated amount from the larger expression before forming the equation.
Frequently asked questions
What is the correct answer to this question?
\(t=9\)
Why is this the correct answer?
“\(C(t)\) is 12 less than \(D(t)\)” means \(C(t)=D(t)-12\). Thus, \(130-5t=70+3t-12\). Simplifying gives \(72=8t\), so \(t=9\). Option \(t=8\) is close, but the difference between the two values is not 12 there. Exam tip: For “less than” comparisons, subtract the stated amount from the larger expression before forming the equation.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
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