If (C(t)=260-9t) and (D(t)=80+5t), at what (t) will (C(t)) be (12) less than (D(t))?
Answer and explanation
Correct answer: \(t=\frac{96}{7}\)
“\(C(t)\) is 12 less than \(D(t)\)” means \(C(t)=D(t)-12\). Thus, \(260-9t=80+5t-12\), or \(260-9t=68+5t\). This gives \(192=14t\), so \(t=\frac{96}{7}\). At \(t=12\), the difference between the two functions is 24, not 12. Exam tip: For “less than by” questions, write the smaller quantity as the larger quantity minus the stated difference.
Frequently asked questions
What is the correct answer to this question?
\(t=\frac{96}{7}\)
Why is this the correct answer?
“\(C(t)\) is 12 less than \(D(t)\)” means \(C(t)=D(t)-12\). Thus, \(260-9t=80+5t-12\), or \(260-9t=68+5t\). This gives \(192=14t\), so \(t=\frac{96}{7}\). At \(t=12\), the difference between the two functions is 24, not 12. Exam tip: For “less than by” questions, write the smaller quantity as the larger quantity minus the stated difference.
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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