Question

Question 1 (1 point)

When does the number 1113 equal 87 in our base 10 system?

Answer 1

4

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

`1(a^3)+1(a^2)+1(a)+3 =87\\a^3+a^2+a = 84\\`

a should be a posiitve integer.

By trial and error we check a =1,2,3,4,5....

We find that when a=4

`4^3+4^2+4 = 64+16+4\\= 84`

Hence base number is 4.