Question 976750
Four digits a, b, c, d
:
Write an equation for each statement:
 The last digit is the double of the first digit.
d = 2a
 The second and third digit are same.
b = c
 Third and fourth digit make the number which is twice the number in the first and second digit.
10c + d = 2(10a + b)
10c + d = 20a + 2b
Replace b with c, replace d with 2a
10c + 2a = 20a + 2c
10c - 2c = 20a - 2a
8c = 18a
4c = 9a
c = {{{9/4}}}a
only one single digit integer solution to this
a = 4, then c = 9
therefore
b = 9
and
d = 2(4) = 8
:
and it would be a number plate: 4998
:
:
We can confirm this in the last statement: 98 = 2(49)