Let the CE be X

Let the ME be Y

Let the EE be Z

the average age of the CE's is c years

the average age of the ME's is m years

the average age of the EE's is e years

The Sum of the total ages is 2160: Equation:

 (1)

And there total average age is 36 so:

 (2)

And the average of CE and ME is 39 so:

 (3)

the average age of the ME’s and EE’s is 32 8/11 ---->360/11

 (4)

the average age of the CE's and EE's is 36 2/3 --->110/3

 (5)

"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"

SO the equation would be:

 (6)

We have 6 equations in our case:

---> Replace equation 2: --> SImplfy that:

X+Y+Z=60 (7)

ANd SInce X+Y+Z=60 replace it with equation 6.





 

And from equation number 1 We can replace Xc+Ym+Ze by 2160:

2160+X+6Y+7Z=2460 

X+6Y+7Z=300(8)

Cross multiply the equations 3 4 and 5.

Xc + Ym = 39(X + Y) (set 1)

Ym + Ze = (360/11)(Y + Z) (set 2)

Xc + Ze = (110/3)(X + Z) (set 3)

Add all the sets to get:

2Xc + 2Ym + 2Ze = (227/3)X + (789/11)Y + (2290/33)Z

Since 33 is the lowest multiple; multiply the whole equation by 33.

 and simplify

66Xc + 66Ym + 66Ze = 2497X + 2367Y + 2290Z

Apply the common factor then subsitute with the first equation:

66(2160)=2497X + 2367Y + 2290Z (9)

So after simplfying we have 7,8,9 unknowns

X+Y+Z=60 (7)

X+6Y+7Z=300  (8)

142560=2497X + 2367Y + 2290Z (9)

Subtract 8 from 7 to get:

5Y+6Z=240

Solve for Y:

y=48-1.2Z (subsitution)

Simplfy throughout using substution and elimination method to get:

X=16, Y=24, Z=20

Plug that throughout the quation and solve for the rest as averages:

If you still need help e-mail me.

Paul.

















 

RELATED QUESTIONS

In an organization there are CE’s, ME’s and EE’s.  The sum of their ages is 2160; the... (answered by AnlytcPhil)

Tommy’s age is six less than Abby’s age. Luke’s age is three more than tommy’s... (answered by josgarithmetic)

A mother is 12 years older than triple the age of her daughter.  The sum of their ages is  (answered by ewatrrr)

There are 45 pupils in a class and their average age is 12years. Find the sum of their... (answered by scott8148,stanbon)

Devaughns Age is two times Sydney’s age .the sum of their ages is 63 what is Sydney’s  (answered by josgarithmetic)

Devaughs age is two times Sydney’s age the sum of their ages is 72 what is Sydney’s... (answered by Alan3354,josgarithmetic)

Ahmed’s age is double Abdul’s. The sum of there ages is 75. Find the age of Ahmed’s  (answered by Alan3354,josgarithmetic,ikleyn)

Carole’s age is five times Joe’s age. The sum of their ages is 18. How old are Carole  (answered by josgarithmetic,ikleyn)

Chloe is 5 years older than Mia and Emma is triple Chloe’s age. Double the sum
of... (answered by josgarithmetic)