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)   (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
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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)  (Show Source):
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