Auditions for a new, upcoming band in Chicago were held with 124 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 28, how many women auditioned?

40
44
70
80

Question

Auditions for a new, upcoming band in Chicago were held with 124 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 28, how many women auditioned?

 40
 44
 70
 80

anonymous · Answer

First set up a system of equations to solve the problem:

m + w = 124
2m - 3w = 28

Solve via elimination:  Multiply the top equations by -2

-2m - 2w = -248
2m - 3w = 28

Add the equations together:

-5w = -220

Divide both sides by -5.

w = 44

Substitute 44 for w in the first equation:

m + 44 = 128

Subtract 44 from both sides:

m = 84

So 44 women auditioned and 84 men auditioned.

anonymous · Answer

Thank you! That helped a lot!