document.write( "Question 30586: In an organization there are CE's, ME's and EE's. The sum of their ages is 2160; the average age is 36; the average age of the CE's and ME's is 39; the average age of the ME's and EE's is 32 8/11; the average age of the CE's and EE's is 36 2/3. If each CE had been 1 year older, each ME 6 years and each EE 7 years older, their average age would have been greater by 5 years. Find the number of each group and their average ages. \n" ); document.write( "
Algebra.Com's Answer #17294 by Paul(988)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "Let the CE be X
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document.write( "Let the ME be Y
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document.write( "Let the EE be Z
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document.write( "the average age of the CE's is c years
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document.write( "the average age of the ME's is m years
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document.write( "the average age of the EE's is e years
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document.write( "The Sum of the total ages is 2160: Equation:
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document.write( " (1)
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document.write( "And there total average age is 36 so:
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document.write( " (2)
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document.write( "And the average of CE and ME is 39 so:
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document.write( " (3)
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document.write( "the average age of the ME’s and EE’s is 32 8/11 ---->360/11
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document.write( " (4)
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document.write( "the average age of the CE's and EE's is 36 2/3 --->110/3
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document.write( " (5)
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document.write( "\"If each CE had been 1 year older, each ME 6 years and each EE 7 years older, their average age would have been greater by 5 years\"
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document.write( "SO the equation would be:
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document.write( " (6)
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document.write( "We have 6 equations in our case:
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document.write( "---> Replace equation 2: --> SImplfy that:
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document.write( "X+Y+Z=60 (7)
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document.write( "ANd SInce X+Y+Z=60 replace it with equation 6.
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document.write( "\"%28X%28c%2B1%29%2BY%28m%2B6%29%2BZ%28e%2B7%29%29%2F60+=+41\"
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document.write( "\"X%28c%2B1%29%2BY%28m%2B6%29%2BZ%28e%2B7%29+=+2460\"
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document.write( "\"Xc%2BX+%2B+Ym%2B6Y+%2B+Ze%2B7Z+=+2460\" 
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document.write( "And from equation number 1 We can replace Xc+Ym+Ze by 2160:
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document.write( "2160+X+6Y+7Z=2460 
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document.write( "X+6Y+7Z=300(8)
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document.write( "Cross multiply the equations 3 4 and 5.
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document.write( "Xc + Ym = 39(X + Y) (set 1)
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document.write( "Ym + Ze = (360/11)(Y + Z) (set 2)
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document.write( "Xc + Ze = (110/3)(X + Z) (set 3)
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document.write( "Add all the sets to get:
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document.write( "2Xc + 2Ym + 2Ze = (227/3)X + (789/11)Y + (2290/33)Z
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document.write( "Since 33 is the lowest multiple; multiply the whole equation by 33.
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document.write( " and simplify
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document.write( "66Xc + 66Ym + 66Ze = 2497X + 2367Y + 2290Z
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document.write( "Apply the common factor then subsitute with the first equation:
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document.write( "66(2160)=2497X + 2367Y + 2290Z (9)
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document.write( "So after simplfying we have 7,8,9 unknowns
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document.write( "X+Y+Z=60 (7)
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document.write( "X+6Y+7Z=300  (8)
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document.write( "142560=2497X + 2367Y + 2290Z (9)
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document.write( "Subtract 8 from 7 to get:
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document.write( "5Y+6Z=240
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document.write( "Solve for Y:
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document.write( "y=48-1.2Z (subsitution)
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document.write( "Simplfy throughout using substution and elimination method to get:
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document.write( "X=16, Y=24, Z=20
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document.write( "Plug that throughout the quation and solve for the rest as averages:
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document.write( "If you still need help e-mail me.
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document.write( "Paul.\r
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