SOLUTION: The sum of three numbers is 63. The 2nd is 3 greater than five times the first, and the 3rd is 4 less than twice the 1st. find the numbers.

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Question 590208: The sum of three numbers is 63. The 2nd is 3 greater than five times the first, and the 3rd is 4 less than twice the 1st. find the numbers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers a, b, and c
given:
(1) +a+%2B+b+%2B+c+=+63+
(2) +b+=+5a+%2B+3+
(3) +c+=+2a+-+4+
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There are 3 equations and 3 unknowns, so it's solvable
Substitute (3) into (1)
(1) +a+%2B+b+%2B+2a+-+4+=+63+
(1) +3a+%2B+b+=+67+
-----------------
(2) +5a+-+b+=+-3+
Add (1) and (2)
(2) +5a+-+b+=+-3+
(1) +3a+%2B+b+=+67+
+8a+=+64+
+a+=+8+
Plug this back into (3)
(3) +c+=+2%2A8+-+4+
(3) +c+=+16+-+4+
(3) +c+=+12+
Plug this into (1)
(1) +a+%2B+b+%2B+12+=+63+
(1) +8+%2B+b+%2B+12+=+63+
(1) +b+=+63+-+20+
(1) +b+=+43+
-------------
check:
(2) +b+=+5a+%2B+3+
(2) +43+=+5%2A8+%2B+3+
(2) +43+=+43+
OK