SOLUTION: (Can someone please help me with this question?) The sum of two numbers is 3. Four times the larger number plus three times the smaller number is 25. Find the numbers. The lar

Algebra ->  Sequences-and-series -> SOLUTION: (Can someone please help me with this question?) The sum of two numbers is 3. Four times the larger number plus three times the smaller number is 25. Find the numbers. The lar      Log On


   



Question 844309: (Can someone please help me with this question?)
The sum of two numbers is 3. Four times the larger number plus three times the smaller number is 25. Find the numbers.
The larger number is___?
and the smaller number is___?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be +a+ and +b+
and assume +b+ is the larger
given:
(1) +a+%2B+b++=+3+
(2) +4b+%2B+3a+=+25+
--------------------
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+4b+=+25+
(1) +-3a+-+3b+=+-9+
--------------------
+b+=+16+
and
(1) +a+%2B+b++=+3+
(1) +a+%2B+16++=+3+
(1) +a+=+-13+
-------------------
+a+=+-13+
+b+=+16+
-----------
check:
(2) +4b+%2B+3a+=+25+
(2) +4%2A16+%2B+3%2A%28-13%29+=+25+
(2) +64+-+39+=+25+
(2) +25+=+25+
OK