Let Jack's age, be J

Then Marie's is: 27 - J, and Fred's is: 38 - J

Also, 27 - J + 38 - J = 33

- J - J + 65 = 33 

- J - J = 33 - 65 

- 2J = - 32

J, or Jack's age is = , or  

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
 .

Hi there,



I was given the following problem and I just can't figure it out. Could you please let me know how to come up with the answer? Thanks!

 

Given these facts: Jack's age plus Marie's age is 27; Jack's age plus Fred's age is 38; Marie's age plus Fred's age is 33. How old is Jack?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~





Let j, m, f be their ages.  Then

j + m = 27,    (1)
j + f = 38,    (2)
m + f = 33.    (3)

The method to solve this system is as follows.

Add equations (1), (2) and (3) (both left sides and right sides). You will get

2*(j + m + f) = 27 + 38 + 33 = 98,   or

j + m + f = 49.    (4)     ( <<<--- 49 =  )

Now, distract equation (1) from (4). You will get

f = 49 - 27 = 22.

Next, distract equation (2) from (4). You will get

m = 49 - 38 = 11.

Finally, distract equation (3) from (4). You will get

j = 49 - 33 = 16.

Answer.  Jack is 16,  Marie is 11,  and  Fred is 22.




The lesson to learn from this solution is this trick for solving this special system of equations.



Actually,  it is the method which works in many other similar cases.  See the lessons



      - The tricks to solve some word problems with three and more unknowns using mental math 



      - Joint-work problems for 3 participants  (Problem 2)



in this site.





 

RELATED QUESTIONS

Can you please help me figure this problem out. I tried and I just can't get it. 57% of... (answered by stanbon)

Hi,
I'm having a hard time figuring out the following word problem, and I was hoping you  (answered by mananth)

please help me figure out this problem. I think I know the answer but I cant figure out... (answered by Earlsdon)

Hi there, I am just stuck on a basic rule I have forgotten. I was given this problem:... (answered by jim_thompson5910)

HELP PLEASE!

I for some reason can not understand how to figure out this problem. 
It  (answered by Alan3354)

Hi, I am really struggling with this word problem involving consecutive integers, I have... (answered by josmiceli)

Hi; I was hoping someone could help me with this problem.

Maximum area.  Jason plans... (answered by stanbon)

Hello, could you please show me how to simplify: A=30,000(1+0.055/2)exponential 2.5 I... (answered by josmiceli)

hi i need help with the following problem:

the cubed root of 2x+7=5  (the five is not... (answered by ewatrrr)