Question 731005
1) A haircut for men costs $15, a haircut for women costs $20, and a haircut for children costs $12.  On a certain day, 70 people spent $1190 on haircuts.  Four more women received haircuts than men and children combined.  How many men, women, and children received haircuts?  For full credit, set up and solve a linear system.  Clearly label any variables you introduce.  Write your answer as a sentence.)

number of men ----------x-------------$15
number of women ----------y-----------$20
number of children -------z------------$12

Number of women= (x+z)+4
y= x+z+4

x+y+z=70
x+x+z+4 +z=70
2x+2z=66
/2
x+z=33......................(1)

15x+20(x+z+4)+12z=1192

15x+20x+20z+80+12z=1190

35x+32z=1110


1.00	x	+	1.00	z	=	33.00	.............1	
Total value								
35.00	x	+	32.00	z	=	1110.00	.............2	
Eliminate	y							
multiply (1)by		-32.00						
Multiply (2) by		1.00						
-32.00	x		-32.00	z	=	-1056.00		
35.00	x	+	32.00	z	=	1110.00		
Add the two equations								
3.00	x				=	54.00		
/	3.00							
x	=	18.00						
plug value of			x	in (1)				
1.00	x	+	1.00	z	=	33.00		
18.00		+		z	=	33.00		
				z	=	33.00		-18.00
				z	=	15.00		
				z	=	15.00		
x=	18		number of  	adults			
z=	15		number of 	children
y=      37              number of women

CHECK

18*15+37*20+15*12=	1190