If (C(t)=350-14t) and (D(t)=80+4t), at what (t) will (C(t)) be (18) less than (D(t))?
Answer and explanation
Correct answer: \(t=16\)
The statement “\(C(t)\) is 18 less than \(D(t)\)” means \(C(t)=D(t)-18\). Thus, \(350-14t=80+4t-18\), giving \(288=18t\) and hence \(t=16\). Checking, \(C(16)=126\) and \(D(16)=144\), so \(C(16)\) is 18 less than \(D(16)\). At \(t=15\), the two values are equal, so it is not correct. Exam tip: for “less than by” questions, subtract the stated difference from the larger quantity.
Frequently asked questions
What is the correct answer to this question?
\(t=16\)
Why is this the correct answer?
The statement “\(C(t)\) is 18 less than \(D(t)\)” means \(C(t)=D(t)-18\). Thus, \(350-14t=80+4t-18\), giving \(288=18t\) and hence \(t=16\). Checking, \(C(16)=126\) and \(D(16)=144\), so \(C(16)\) is 18 less than \(D(16)\). At \(t=15\), the two values are equal, so it is not correct. Exam tip: for “less than by” questions, subtract the stated difference from the larger quantity.
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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