SOLUTION: A two-digit number is such that its tens digit is greater than its unit digit by 4. The two-digit number is less than 4 times the product of its digits by 11. Find the number

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Question 1205571: A two-digit number is such that its tens digit is greater than its unit digit by 4. The two-digit number is less than 4 times the product of its digits by 11. Find the number
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A two-digit number is such that its tens digit is greater than its unit digit by 4.
The two-digit number is less than 4 times the product of its digits by 11. Find the number
~~~~~~~~~~~~~~~~~~~~~~ 


The condition is ambiguous. 


If the digits are "a" and "b"  (where "a" is the tens' digit, "b" is the ones digit),
then the second condition can be interpreted in two different ways


    (a)  EITHER  N <  4*a*b*11

    (b)  OR      N <  4*a*b - 11.


Strictly saying, in English, only interpretation (a) corresponds to the text 
written in the post, but it leads to several possible answers.


In order interpretation (b) be valid, the wording must be changed:  

    "The two-digit number is 11 less than 4 times the product of its digits."

Since the condition is ambiguous, this post can not be considered as a Math problem.

Typical soup of words, which does not deserve serious consideration.



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


Although the re-wording of the problem as suggested by the other tutor would make the problem easier to read, there is in fact no ambiguity in the given wording.

"A is less than B by 11" means exactly the same thing as "A is 11 less than B".

To solve the problem as stated....

Let x be the units digit
Then x+4 is the tens digit

The 2-digit number is then

The product of the digits is

The two-digit number is less than 4 times the product of its digits by 11:






x = 3 or x = -17/4; of course the negative solution makes no sense in the problem.

So the units digit is x=3 and the tens digit is x+4=7.

ANSWER: 73

CHECK:
product of digits: 7*3 = 21
4 times product of digits: 4*21 = 84
11 less than 4 times product of digits: 84-11 = 73
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
u, the ones digit
t, the tens digit
10t+u, the two-digit number

, exact translation into symbolism

, substitution of t









The PLUS 29 works.

This means tens digit, .
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