SOLUTION: When the sum of A and B is 87, the sum of B and C is 69, and the sum of C and A is 72. Find out what are A B C are

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Question 1071241: When the sum of A and B is 87, the sum of B and C is 69, and the sum of C and A is 72. Find out what are A B C are
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
When the sum of A and B is 87, the sum of B and C is 69, and the sum of C and A is 72. Find out what are A B C are
~~~~~~~~~~~~~~~~~~~~~~~

You are given

A + B = 87,    (1)
B + C = 69,    (2)
C + A = 72.    (3)

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

2(A + B + C) = 87 + 69 + 72 = 228.

Hence,

A + B + C = 114.    (4)

Now subtract equation (2) from (4). You will get

A = 114 - 69 = 45.

Next, subtract equation (3) from (4). You will get

B = 114 - 72 = 42.

Finally, subtract equation (1) from (4). You will get

C = 114 - 87 = 27.

Answer.  A = 45,  B = 42,  C = 27.

Solved.


It is a standard and very well known trick for such problems.  By applying it,  you can solve the problem mentally.
See the lesson
    - The tricks to solve some word problems with three and more unknowns using mental math
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"3x3-Matrices, determinants, Cramer's rule for systems in three unknowns".


Also, see the lessons
    - Joint-work problems for 3 participants
    - How many coconuts are there in each of five baskets?
from my other textbook
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.
under the topics "Rate of work and Joint-work problems" and "Miscellaneous word problems", respectively.


What "josgarithmetic" proposed in his post is the example of the method you should  NEVER  apply for such problems.

This problem is a very good test to check if the person/the student is mathematically educated or not.

Mathematically educated must know this trick and will use it.
Mathematically non-educated (or mathematically illiterated) will do it as "josgarithmetic" does.


In this sense this problem is a good test for mathematical literacy at an interview.


Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
system%28A%2BB=87%2CB%2BC=69%2CA%2BC=72%29

system%28B=87-A%2CB=69-C%29

-
87-A=69-C
-A%2BC=69-87
A-C=87-69
A-C=18

-
Revised system:
system%28A-C=18%2CA%2BC=72%29-----ready for use of Elimination Method for A and C.
system%28highlight%28A=45%29%2Chighlight%28C=27%29%29

Now find B.
B=87-A
B=87-45
highlight%28B=42%29