SOLUTION: the digit in tens place of a two digit no. is 3 less than the digit in its units place. find the number of the quotient obtained when the number is divided by the sum of it's digit

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Question 1119797: the digit in tens place of a two digit no. is 3 less than the digit in its units place. find the number of the quotient obtained when the number is divided by the sum of it's digit is 4
Found 4 solutions by solver91311, MathTherapy, ikleyn, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the 10s digit and represent the 1s digit.

We then know the following facts:



The number is represented by:



And:



Then





Solve the 2X2 system for and.


John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552) About Me  (Show Source):
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the digit in tens place of a two digit no. is 3 less than the digit in its units place. find the number of the quotient obtained when the number is divided by the sum of it's digit is 4
Let the units digits be U

Then tens digit = U – 3

We then get: matrix%281%2C3%2C+%2810%28U+-+3%29+%2B+U%29%2F%28U+%2B+U+-+3%29%2C+%22=%22%2C+4%29

matrix%281%2C3%2C+%2810U+-+30+%2B+U%29%2F%282U+-+3%29%2C+%22=%22%2C+4%29

matrix%281%2C3%2C+%2811U+-+30%29%2F%282U+-+3%29%2C+%22=%22%2C+4%29

11U - 30 = 4(2U – 3) ------- Cross-multiplying

11U – 30 = 8U – 12

11U – 8U = - 12 + 30

3U = 18

U, or units digit = matrix%281%2C3%2C+18%2F3%2C+or%2C+6%29

Tens digit: 6 – 3, or 3

highlight_green%28matrix%281%2C2%2C+%22Number%3A%22%2C+36%29%29

Answer by ikleyn(52780) About Me  (Show Source):
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.
the digit in tens place of a two digit no. is 3 less than the digit in its units place.
find the number highlight%28cross%28of%29%29 if the quotient obtained when the number is divided by the sum of it's digit is 4
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It is how the condition must be edited to make sense.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Certainly a solution using formal algebra can be a good exercise; however, note that if this were a question on a competitive exam where speed is important, the answer can be found much more quickly using trial and error.

14/(1+4) = 4? Nope.
25/(2+5) = 4? Nope.
36/(3+6) = 4? Yep. Done.

Note further that a very experienced problem solver might solve the problem even faster by noting that, since the number divided by the sum of its digits is 4, the number has to be divisible by 4. The only2-digit number with tens digit 3 less than the units digit that is divisible by 4 is 36.