Auditions for a new, upcoming band in Chicago were held with 102 men and women trying out for the lead singer position. If twice the number of men less three times the number of women is equal to -6, how many women auditioned? Answer 40 60 42 38

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i guess you are supposed to write an equation in two variables. put say \(m\) as the number of men and \(w\) as the number of women, then the two equations will be \[m+w=102\] \[2m-3w=-6\]

there are a couple of ways to solve one is to solve the first equation for \(w\) as \(w=102-m\) and then substitute in to the second equation to get \[2m-3(102-m)=-6\] and solve for \(m\) \[2m-306+3m=-6\] \[5m-306=-6\] \[5m=300\] \[m=60\] and so \[w=42\]

i get 60 men and 42 women

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