Answer to Question #241948 in Statistics and Probability for mani

Question

if the arithmetic mean and geometric mean of three numbers a,b and c are 19 and 15 respectively. find value of a and b when c=27.

Answer 1

If the mean of $a+b+c = 19$ , the sum of three numbers is $19*3 = 57.$

Given that the geometric mean of the three numbers is the cube root of $(a*b*c) = 15, 15^3=3375.$

Factoring 3375 yields $3*3*3*5*5*5.$

If $c=27 (3*3*3)$ then $a=5, b=25 \space or \space a=25, b=5.$

Mean of $a+b+c = \frac{(5+25+27)}{3} = 19.$

Geometric mean =$\frac{(5*25*27)}{3} = 15.$