SOLUTION: One number is 7 more than another number. Find the two numbers if three times the larger number exceeds four times the smaller number by 5. No clue where to start or begin!!!

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Question 168241This question is from textbook Principles of Elementary Algebra with Applications
: One number is 7 more than another number. Find the two numbers if three times the larger number exceeds four times the smaller number by 5.

No clue where to start or begin!!! Help me please!!!! Thank you!!
This question is from textbook Principles of Elementary Algebra with Applications

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the larger number a
Call the smaller number b
Given:
(1) a+=+b+%2B+7
(2) 3a+=+4b+%2B+5
Substitute a in (1) for a in (2)
(2) 3%2A%28b+%2B+7%29+=+4b+%2B+5
3b+%2B+21+=+4b+%2B+5
Subtract 3b from both sides
Subtract 5 from both sides
b+=+16
and, since
(1) a+=+b+%2B+7
a+=+16+%2B+7
a+=+23
The larger number is 23 and the smaller number is 16
check:
(1) a+=+b+%2B+7
23+=+16+%2B+7
23+=+23
(2) 3a+=+4b+%2B+5
3%2A23+=+4%2A16+%2B+5
69+=+64+%2B+5
69+=+69
OK