SOLUTION: One number is 6 more than another. If the sum of the smaller number and 3 times the larger number is 34, find the two numbers.

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Question 63641: One number is 6 more than another. If the sum of the smaller number and 3 times the larger number is 34, find the two numbers.
Answer by joyofmath(189) About Me  (Show Source):
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One number is 6 more than another. If the sum of the smaller number and 3 times the larger number is 34, find the two numbers.


Let S = the smaller number and L = the larger one.
Then, S%2B3L=34 and L=S%2B6.
Replace L with S+6 in the first equation:
Then, S%2B3%28S%2B6%29=34 or S%2B3S%2B18=34.
So, 4S=16 or highlight%28S=4%29.
So, the smaller number is 4. The larger is 6 more than 4 so the larger number = 10.
To verify that the numbers are 4 and 10 we note the the sum of the smaller number and three times the larger number is 4%2B3%2810%29+=+4%2B30+=+34.