Question 83487: If I have six fish in each tank and 1 fish left over. If have seven in each tank and 1 tank left over, how many fish and how many tanks do I have?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let T = the number of tanks and F = the number of fish.
From the problem description, you have 6 fish per tank plus one fish, (6 X T + 1) fish, so you can write:
1) 6T+1 = F
You also know that if you put 7 fish per tank, you can use one less tank, so you have (7(T-1)) fish, so you can write:
2) 7(T-1) = F Setting these two equations equal to each other, you can solve for T, the number of tanks.
6T+1 = 7(T-1) Simplify and solve for T.
6T+1 = 7T-7 Add 7 to both sides.
6T+8 = 7T Subtract 6T from both sides.
T = 8
You have 8 tanks.
To find the number of fish, substitute this value of T into either equation 1) or equation 2) and solve for F.
1) F = 6T+1 Substitute T = 8.
F = 6X8+1
F = 48+1
F = 49
Or...
2) F = 7(T-1) Substitute T = 8.
F = 7(8-1)
F = 7X7
F = 49
You have 49 fish.
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