The average of X1, X2 and X3 is 14. Twice the sum of X2 and X3 is 30. What is the value of X1 ?

The average condition gives (X1+X2+X3)/3 = 14, so the total X1+X2+X3 = 42, using the arithmetic mean formula [1]. The second condition, “twice the sum of X2 and X3 is 30,” implies 2·(X2+X3)=30, hence X2+X3=15. Substituting this into the total sum yields X1 = 42 − (X2+X3) = 42 − 15 = 27. This is a straightforward application of basic linear substitution as used when solving simple systems of linear equations: determine one combined quantity and subtract to find the remaining variable [2]. Thus X1 = 27, corresponding to option 2.

Sources

1. [1] https://faculty.sites.iastate.edu/ahallam/files/inline-files/BasicStat.pdf
2. [2] https://users.math.msu.edu/users/parker/309/Leon_Sections1-5.pdf