What's this???

Geometry Level pending

If $a^3b=abc=180$ and $a,b,c$ are positive integers, then value of $c$ is

25 15 None 110

1 solution

Vaibhav Kandwal
Dec 17, 2014

Since $a,b,c$ are positive integers and $180$ is not divisible by any $2^3, 3^3, 4^3$ and $5^3$ .

So $a^3b=180$ is possible only when $a^3=1$ and $b=180$ .

Thus $a=1$ and $b=180$ .

Now $a^3b=abc \Rightarrow c=a^2=1$

Finally, $\boxed{c=1}$ , Therefore answer is $\boxed{None}$

I just divided both $15$ and $25$ to $180$ and check if the resulting value for a is an integer.

Marc Vince Casimiro - 6 years, 5 months ago