SOLUTION: I'm struggling with this problem... The sum of an integer and twice a smaller integer is 14. if the smaller integer is subtracted from twice the larger integer, the differences i

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: I'm struggling with this problem... The sum of an integer and twice a smaller integer is 14. if the smaller integer is subtracted from twice the larger integer, the differences i      Log On


   



Question 1054564: I'm struggling with this problem...
The sum of an integer and twice a smaller integer is 14. if the smaller integer is subtracted from twice the larger integer, the differences is 8. what are the two integers?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the larger integer = +a+
Let the smaller integer = +b+
-------------------------------
(1) +a+%2B+2b+=+14+
(2) +2a+-+b+=+8+
-----------------------
Multiply both sides of (2) by +2+
and add (1) and (2)
(2) +4a+-+2b+=+16+
(1) ++a+%2B+2b+=+14+
---------------------
+5a+=+30+
+a+=+6+
and
(1) +a+%2B+2b+=+14+
(1) +6+%2B+2b+=+14+
(1) +2b+=+8+
(1) +b+=+4+
----------------------
The integers are 6 and 4
----------------------
check:
(2) +2a+-+b+=+8+
(2) +2%2A6+-+4+=+8+
(2) +12+-+4+=+8+
(2) +8+=+8+
OK