SOLUTION: Each day Sam the dog drinks half of the water remaining in his bowl. His owner then adds 200 ml to the bowl.there was 500 ml of water in the bowl at the end of Thursday. How much w

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Question 1132768: Each day Sam the dog drinks half of the water remaining in his bowl. His owner then adds 200 ml to the bowl.there was 500 ml of water in the bowl at the end of Thursday. How much water was in the bowl at the start of Wednesday

Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = ml of water at the start of
Wednesday
At the end of Wednesday, there is
+x+-+%281%2F2%29%2Ax+%2B+200+=+%281%2F2%29%2Ax+%2B+200+ ml
in Sam's bowl
At the end of Thursdays, sam has:
+%281%2F2%29%2Ax+%2B+200+-+%281%2F2%29%2A%28+%281%2F2%29%2Ax+%2B+200+%29+
+%281%2F2%29%2Ax+%2B+200+-+%281%2F4%29%2Ax+-+100+
+%281%2F4%29%2Ax+%2B+100+
You are told that:
+%281%2F4%29%2Ax+%2B+100+=+500+
+%281%2F4%29%2Ax+=+400+
+x+=+1600+
There was 1600 ml at the start of Wednesday
--------------------------------------------------
check:
Sam drinks half, so 800 ml is left
200 ml is added, so Sam has 1000 ml
at end of Wednesday
Sam drinks half, so 500 ml is left at end
of Thursday
OK

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


In most problems like this, working backwards is an easier approach. This is especially true if the number of steps is large.

The algebraic approach shown by the other tutor would be extremely cumbersome if you were asked to find the amount in the bowl at the beginning of Monday; working backwards to find the amount in the bowl at the beginning of Monday would still be relatively easy.

Working backwards then...

There are 500ml left in the bowl at the end of Thursday; since the dog drank half of what was in his bowl at the beginning of the day, there were 500*2 = 1000ml at the beginning of Thursday.

Since there were 1000ml at the beginning of Thursday, and since the dog's owner added 200ml at the end of Wednesday, there were 1000-200 = 800ml at the end of Wednesday.

Since there were 800ml left in the bowl at the end of Wednesday, and since the dog drank half of what was in his bowl at the beginning of the day, there were 800*2 = 1600ml at the beginning of Wednesday.

ANSWER: 1600ml at the beginning of Wednesday.