SOLUTION: If the larger of two numbers is 3 more than 3 times the smaller. If the smaller number is subtracted from the larger and the result is 15, what are the two numbers ? I am having t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the larger of two numbers is 3 more than 3 times the smaller. If the smaller number is subtracted from the larger and the result is 15, what are the two numbers ? I am having t      Log On


   



Question 629384: If the larger of two numbers is 3 more than 3 times the smaller. If the smaller number is subtracted from the larger and the result is 15, what are the two numbers ?
I am having the hardest time with these word problems no matter what I do I get the wrong answer, Please help me ?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st thing to do is define the unknowns
Let +a+ = the larger of the 2 numbers
Let +b+ = the smaller of the 2 numbers
given:
(1) +a+=+3b+%2B+3+
( The larger of two numbers is 3 more than 3 times the smaller. )
(2) +a+-+b+=+15+
( If the smaller number is subtracted from the larger, the result is 15. )
---------------
There are 2 equations and 2 unknowns, so
the problem is solvable.
Substitute (1) into (2)
(2) +3b+%2B+3+-+b+=+15+
(2) +2b+%2B+3+=+15+
(2) +2b+=+12+
(2) +b+=+6+
and, since
(1) +a+=+3b+%2B+3+
(1) +a+=+3%2A6+%2B+3+
(1) +a+=+18+%2B+3+
(1) +a+=+21+
The numbers are 21 and 6
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check:
(1) +a+=+3b+%2B+3+
(1) +21+=+3%2A6+%2B+3+
(1) +21+=+18+%2B+3+
(1) +21+=+21+
and
(2) +a+-+b+=+15+
(2) +21+-+6+=+15+
(2) +21+=+15+%2B+6+
(20 +21+=+21+
OK