SOLUTION: 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

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.)
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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

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