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Chapter 14: Problem 20

If 16 is the average (arithmetic mean) of \(p, 24,\) and \(q,\) what is \(16(p+q) ?\) a. 180 b. 192 c. 384 d. 524 e. 768

Short Answer

Expert verified
The value of \(16(p+q)\) is 384. So, the correct answer is (c) 384.

Step by step solution

01

Applying average formula

An average of a set of numbers is the sum of those numbers divided by the quantity of numbers. So, we can write this in equation form: \(\frac{p+24+q}{3}=16\).
02

Solving for p+q

Rearrange the equation from previous step to find the sum of p and q: Multiply both sides by 3, resulting in \(p + 24 + q = 48\). Subtract 24 from both sides to find \(p+q\), resulting in \(p + q = 24\).
03

Substitution into \(16(p+q)\)

Substitute \(p+q\) into \(16(p+q)\) and calculate the value: \(16 \times 24 = 384\).

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