Auditions for a play in New York were held with 100 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 20, how many women auditioned?
A. 44
B. 36
C. 76
D. 60

Question

Auditions for a play in New York were held with 100 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 20, how many women auditioned?
A. 44
B. 36
C. 76
D. 60

anonymous · Answer

twice the # of men minus 3 times the # of women = 20
men + women = 100
Write your equations and solve the system of equations.

mathstudent55 · Answer

Use the variable m to represent the number of men, and the variable w to represent the number of women.

From the total number of applicants, you get
m + w = 100

From this statement:
"twice the number of men less three times the number of women is equal to 20",
you get this equation:

2m -3w = 20

Now you have a system of two equations in two variables that you need to solve.

m + w = 100
2m -3w = 20

Do you know how to solve it, or do you need help?

anonymous · Answer

can you help me solve it please?

mathstudent55 · Answer

Sure.

mathstudent55 · Answer

m + w = 100
2m -3w = 20

Let's use the substitution method.
In this method, you solve one equation for one variable, then you plug that into the other equation.

Let's solve the first equation for m.
Subtract w from both sides to get:
m = 100 - w

Are you ok so far?