emmak wrote:

The average weight of a class is x pounds. When a new student weighing 80 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

A. 85

B. 86

C. 88

D. 90

E. 92

(All weights are in pounds.)

\(? = x\)

Excellent opportunity to use the

homogeneity nature of the average:

\(\sum\nolimits_n { = \,\,nx\,\,\,\,\,\left( {n\,\,{\rm{students}}} \right)}\)

\(\left\{ \matrix{

80 + \sum\nolimits_n {\, = \sum\nolimits_{n + 1} {\, = \,\,\left( {n + 1} \right)\left( {x - 1} \right)} } \hfill \cr

110 + \sum\nolimits_n {\, = \sum\nolimits_{n + 1} {\, = \,\,\left( {n + 1} \right)\left( {x + 4} \right)} } \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,110 - 80 = \left( {n + 1} \right)\left[ {\left( {x + 4} \right) - \left( {x - 1} \right)} \right]\)

\(30 = 5\left( {n + 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 5\)

\(80 + 5x = \left( {5 + 1} \right)\left( {x - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 86\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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