SOLUTION: Hi One large tank holds 300litres more than the smaller tank.if the smaller tank is 2/3 full, it holds as much as the larger tank when the larger tank is half full.what is the cap

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Question 1090954: Hi
One large tank holds 300litres more than the smaller tank.if the smaller tank is 2/3 full, it holds as much as the larger tank when the larger tank is half full.what is the capacity of each.
Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = capacity of the smaller tank in litres
Let +b+ = capacity of the larger tank in litres
--------------------------------------------
(1) +b+=+a+%2B+300+
(2) +%282%2F3%29%2Aa+=+%281%2F2%29%2Ab+
----------------------------
Multiply both sides of (2) by +6+
(2) +4a+=+3b+
Plug (1) into (2)
(2) +4a+=+3%2A%28+a+%2B+300+%29+
(2) +4a+=+3a+%2B+900+
(2) +a+=+900+
and
(1) +b+=+a+%2B+300+
(1) +b+=+900+%2B+300+
(1) +b+=+1200+
----------------------
The smaller tank holds 900 litres
The larger tank holds 1200 liters
--------------------------------
check:
(2) +%282%2F3%29%2Aa+=+%281%2F2%29%2Ab+
(2) +%282%2F3%29%2A900+=+%281%2F2%29%2A1200+
(2) +600++=+600+
OK