Four-digit number

Juraj is thinking of a four-digit number that he told us about:

(a) Its digit sum is one hundredth of the number that I get by rounding the imaginary number to hundreds.
(b) Its last digit is 1 more than the second-to-last.
(c) The sum of its last two digits is equal to its second digit.

What number is Juraj thinking of?

Correct answer:

x =  4000

Step-by-step explanation:

x = 1000a+100b+10c+d  a+b+c+d = (1000a+100b)/100 d=c+1 c+d=b  b>5  a+b+c+d = (1000a+100(b+1))/100 d=c+1 c+d=b  b = c+d = c+c+1 = 2c+1  100(a+b+c+d) = 1000a+100b+100  100(a+b+c+c+1) = 1000a+100b+100  100(a+2c+1+c+c+1) = 1000a+100(2c+1)+100  a=2 c=9  b=2 c+1=2 9+1=19 d=c+1=9+1=10  x=1000 a+100 b+10 c+d=1000 2+100 19+10 9+10=4000



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