Answer:
4
Step-by-step explanation:
We are given a number 1113 to some base which equals 87to base 10
Let the base be equal to a
Then using place value for 1113 to base a we get
[tex]1(a^3)+1(a^2)+1(a)+3 =87\\a^3+a^2+a = 84\\[/tex]
a should be a posiitve integer.
By trial and error we check a =1,2,3,4,5....
We find that when a=4
[tex]4^3+4^2+4 = 64+16+4\\= 84[/tex]
Hence base number is 4.
