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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 answer is c. 384.

Step by step solution

01

Set up the equation

The average of \(p, 24, q\) is 16. So the formula for calculating an average can be written as \((p + 24 + q) / 3 = 16.\)
02

Solve for the sum of p and q

Solve the equation above for \(p+q\). Multiply each side of the equation by 3 to get rid of the fraction: \(p + 24 + q = 48.\) Then, subtract 24 from each side to isolate \(p+q\): \(p+q = 24.\)
03

Calculate \(16(p+q)\)

Substitute the value for \(p+q\) into the equation \(16(p+q)\). This gives \(16 * 24 = 384\)

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