Motoring1 min ago
Number Problem
4 Answers
What number, when added to a number Ten times bigger gives a number which,
When its first digit is multiplied by Four and again added to the result = 1000
When its first digit is multiplied by Four and again added to the result = 1000
Answers
1 to 4 of 4
Best Answer
No best answer has yet been selected by Dee-M-See. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.
The second bit of the puzzle relates to the value of 4a, for any number with the integers ab, which clearly must be less than or equal to 36 (since a can't be any bigger than 9). Consequently, the number x (which =ab), must be greater than or equal to 88, since x + 10x has to be greater than or equal to 964, i.e. 11x must be greater than or equal to 964 (i.e. 1000-36).
So, we can test the value of the integer a simply by knowing that it can only be 8 or 9; simply looking at a=9, we can readily see that 4a=36, but we know that the value of 11x would be >990, as ab>90. This means that the integer a must be 8. Now we only have two choices of b=8 or 9; testing again shows that x=ab=88, since we know that for x=89, then 11x would be 979 and would not equal 1000-4a.
We can prove this by calculating 11x=968 and 4a=32, i.e. we meet the conditions required.
So, we can test the value of the integer a simply by knowing that it can only be 8 or 9; simply looking at a=9, we can readily see that 4a=36, but we know that the value of 11x would be >990, as ab>90. This means that the integer a must be 8. Now we only have two choices of b=8 or 9; testing again shows that x=ab=88, since we know that for x=89, then 11x would be 979 and would not equal 1000-4a.
We can prove this by calculating 11x=968 and 4a=32, i.e. we meet the conditions required.
1 to 4 of 4
