Question

In the land of Alpha, (1/4)X(32)=5. What is (1/3)X(10)?
A. 1
B. 2
C. 3
D. 4

Answer 1

I assume this means 32 is not base 10. We need to find the base.
32 = 3*x +2

whatever the base, it is more than 5.
multiply both sides by 4
3x+2 = 4*5=20(base 10)
solve for x
3x= 18
x=6

base 6 works.

now (1/3) * 10(base 6) is 1/3 * 6 =2

Answer 2

I don't understand how you got the formula to find the base.

Answer 3

Why do you solve for 32?

Answer 4

Can you solve for the 1/4 or only just 32 to find the base?

Answer 5

Example: a number abc in base 10 represents a*10^2 + b*10 + c
abc in base x represents a*x^2 + b*x +c

if we have just 2 digits: ab, this in base x stands for a*x + b

Answer 6

I understand that.

Answer 7

10 in base x represents the number x
all numbers less than x will use one symbol. since they use 5, the base is bigger than 5 (and 4)

so it safe to say 4 is the same in base x or in base 10 (it is four) and ditto for 5

we can still do algebra, so
4*1/4 * (3x+2) = 4*5

4/4 is one (even in base x)
4*5 is 20 in base 10

Answer 8

So how do we solve that for the second part?

Answer 9

I changed everything to base 10 to do the arithmetic. then change the answer back to base 6

Answer 10

Ok. I understand. Thank you!