Four-digit - sum

A four-digit number has a digit sum of 20. The sum of its last two digits equals the second digit increased by 5. The sum of the first and last digits equals the second digit decreased by 3. If we write the digits of this number in reverse order, the number increases by 2,178. Find this number.

Final Answer:

x =  1793

Step-by-step explanation:

x=abcd = 1000a+100b+10c + d a+b+c+d=20 c+d = b+5 a+d=b3 dcbaabcd=2178  a=0 , d=0 d>a da=2  c+d = b+5 a+d = b3 ac = 35 ac = 8  c = a+8 0 a,b,c,d9  0c=a+8 9 0a+8 9 80a98 1a1  a=1 c=a+8=1+8=9 d=a+2=1+2=3 b=20acd=20193=7  1+7+9+3=20 9+3 = 7+5 1+3=73 39711793=2178  x=1793



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