SOLUTION: I need help with this question: 3 times the number B is equal to 4 times the number A. The sum of 6 times B and 2 times A is 90. What is A and B?

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Question 1075986: I need help with this question: 3 times the number B is equal to 4 times the number A. The sum of 6 times B and 2 times A is 90. What is A and B?
Found 2 solutions by addingup, josmiceli:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
3B = 4A therefore 3b-4A = 0 Now multiply all sides times -1:
-3B+4A = 0 Add this equation to the equation below
:
6B+2A = 90 divide all sides by 2
3B+A = 45
------------------------
3B+A = 45
+
-3B+4A = 0
----------
0B+5A = 45 since 0B is 0, we can rewrite:
5A = 45
A = 9
Now solve for B:
3B = 4(9)
3B = 36
B = 12
------------------------------------
Check:
3B = 4A
3(12) = 4(9)
36 = 36 correct
The other equation:
6B+2A = 90
6(12)+2(9) = 90
72+18 = 90 Also correct
email me if there is anything you don't understand.
John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) +3B+=+4A+
(2) +6B+%2B+2A+=+90+
----------------------------
I will multiply both sides of (1) by +2+
(1) +6B+=+8A+
Now I can substitute (1) into (2)
(2) +8A+%2B+2A+=+90+
(2) +10A+=+90+
Divide both sides by +10+
(2) +A+=+9+
Now put this result back into (1)
(1) +3B+=+4A+
(1) +3B+=+4%2A9+
(1) +3B+=+36+
(1) +B+=+12+
-------------------
+A+=+9+
+B+=+12+
------------------
check:
(2) +6B+%2B+2A+=+90+
(2) +6%2A12+%2B+2%2A9+=+90+
(2) +72+%2B+18+=+90+
(2) +90+=+90+
OK
You can check (1)