SOLUTION: the sum of two numbers is 19. if 5 times the smaller number is 3 less than twice the larger number, what are the two numbers? thanks God bless.

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Question 587059: the sum of two numbers is 19. if 5 times the smaller number is 3 less than twice the larger number, what are the two numbers?
thanks God bless.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be a and b
given:
(1) +a+%2B+b+=+19+
Let +b+ = the smaller number
(2) +5b+=+2a+-+3+
(2) +b+=+%28+2a+-+3+%29+%2F+5+
Substitute (2) into (1)
(1) +a+%2B+%28+2a+-+3+%29%2F5+=+19+
(1) +5a+%2B+2a+-+3+=+5%2A19+
(1) +7a+=+95+%2B+3+
(1) +7a+=+98+
(1) +a+=+14+
and, since
(1) +a+%2B+b+=+19+
(1) +14+%2B+b+=+19+
(1) +b+=+5+
The numbers are 5 and 14
check:
(2) +5b+=+2a+-+3+
(2) +5%2A5+=+2%2A14+-+3+
(2) +25+=+28+-+3+
(2) +25+=+25+
OK