Dividends and Divisors
Find an integer value of x such that when 3 x − 3 9 is divided by 2 x , the quotient is 1 and the remainder is 5 0 .
The answer is 89.
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8 solutions
tnx
Great, i was doing 3x-39+50/2x=1 .. how stupid i am :p
oh now i see it..i didnt know what i have to do with the reminder :p
what about 50
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50 is remainder. so 50 is like an excess value because of which 3x-39 can not be divided without a remainder. so if you subtract 50 from 3x-39 it will be properly divisible and then quotient will be 1
Thank you! :)
Wow Thanks
tnx
Please put this in simpler form
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Simpler? I think this is the simplest form
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I think Kabir Bagai meant using LateX to format the answer. But thanks for the answer anyway!
Each division can be defined as: D i v i s o r D i v i d e n d = Q u o t i e n t × D i v i s o r + R e m a i n d e r
When 3 x − 3 9 is divided by 2 x , the result is an improper fraction with 1 whole part(quotient) and 5 0 / 2 x fractional part.(remainder)(also, 3x - 39 = 1 * 2x + 50 ).
So, we have, 2 x 3 x − 3 9 = 1 2 x 5 0 o r , 2 x 3 x − 3 9 = 2 x 2 x + 5 0 o r , 3 x − 3 9 = 2 x + 5 0 o r , x = 8 9
I would have never thought of solving it this way. Thanks!
This was the most 'intuitive' approach since I am a little bad at maths. Please don't vote if you think this is useless or unwise.
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Can you check that you wrote what you mean?
I think your first line is wrong.
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Sir you mean this line is wrong? 2 x 3 x − 3 9 = 1 × 2 x 5 0
I can explain this one as follows:
Any real number can be expressed like Dividend = Quotient * Divisor + Remainder. So, 3 x − 3 9 = 2 x × 1 + 5 0 which can be evaluated to x = 8 9
I just wrote it as 1 × 2 x 5 0 just to make it more obvious and clearer.
I believe your first line is not accurate, as Dividend=Quotient×Divisor+Remainder
We can easily get the answer by using E u c l i d ′ s D i v i s i o n A l g o r i t h m which states that for any two integers a and b where b = 0 there exists unique integers q and r such that,
a = b × q + r o r D i v i d e n d = Q u o t i e n t × D i v i s o r + R e m a i n d e r
Now applying E u c l i d ′ s D i v i s i o n A l g o r i t h m , we get ,
3 x − 3 9 = ( 2 x ) × 1 + 5 0
⇒ 3 x − 2 x = 5 0 + 3 9
x = 8 9
(3x -39)/2x = 1 + (50/2x) since 50 is the remainder
3x - 39 = 2x + 50
x = 89
(3x-39)/2x gives quotient 1 and remainder x-39
since the remainder is 50 then
x-39=50
x=89
where does the remainder x-39 come from in the first sentence?
Dividend=(Divisor*Quotient)+Remainder
3x-39=(2x*1)+50 ==>3x-2x=50+39 ==>x=89 Answer
let say we have 30 is divided by 7, the quotient is 4 and the remainder is 2... the format is : 30 = (divider x quotient) + remainder
based on the explanation we get : 3x - 39 = 2x + 50 so that, x = 89
In order to solve this, first disregard the remainder of 50 completely, and set it up so that the equation equals one.
3x - 39 \ 2x = 1
Now it's as if you're solving a simple equation.
1: multiply both sides by 2x
3x - 39 = 2x
2: Subtract 2x from both sides
x - 39 = 0
3: Add 39 to both sides
x = 39
4: Now add 50 to x, and the solution is 89. The reason we do this is because we want a remainder of 50. Already, if we plug in 39 to the equation, we get a quotient of one. However, in order to get a remainder of 50, we have to do that extra addition to have 50 left over.
the problem says when we divide 3x-39 by 2x remainder is 50. So 3x-39-50 or, 3x-89 is divided by 2x without any remainder and then quotient would be 1. So