Value of B in this ratio problem?

Question

a,b,c integers

$a+b+c=45$

$\frac{a}{b}=\frac{3}{2}$

$\frac{b}{c}=\frac{4}{5}$

b=?

Answer 1

$a=\frac{3}{2}b$, $c=\frac{5}{4}b$, therefore $45=a+b+c=\frac{3}{2}b+b+\frac{5}{4}b=\frac{6+4+5}{4}b=\frac{15}{4}b$ and we get $b=45 \cdot \frac{4}{15}=12$

Answer 2

Use that $$a=\frac{3}{2}b$$ and $$c=\frac{5}{4}b$$