SOLUTION: The difference between three times one number and a lesser one is 37. The sum of the greater number and twice the lesser number is 38. Find the numbers. Please include a "let state

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Question 176895: The difference between three times one number and a lesser one is 37. The sum of the greater number and twice the lesser number is 38. Find the numbers. Please include a "let statement.".
Found 2 solutions by josmiceli, Fombitz:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the larger number = a
Let the smaller number = b
given:
(1) 3a+-+b+=+37
(2) a+%2B+2b+=+38
-----------------
Multiply (1) by 2 and
add (1) and (2)
(1) 6a+-+2b+=+74
(2) a+%2B+2b+=+38
-----------------------
7a+=+112
a+=+16
And since
(2) a+%2B+2b+=+38
16+%2B+2b+=+38
2b+=+22
b+=+11
The numbers are 16 and 11
check:
(1) 3%2A16+-+11+=+37
48+-+11+=+37
37+=+37
OK

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the first (greater) number and let B be the second (lesser) number.
"difference between three times one number and a lesser one is 37"
1.3A-B=37
"sum of the greater number and twice the lesser number is 38"
2.A%2B2B=38
From eq. 1,
1.3A-B=37
B=3A-37
Substitute that into eq. 2 and solve for A,
2.A%2B2B=38
A%2B2%283A-37%29=38
A%2B6A-74=38
7A=116
highlight%28+A+=16%29
Use eq.1,
B=3A-37
B=3%2816%29-37
B=48-37
highlight%28B=11%29