Suppose the ratio of Lev's age to Mina's age is and the ratio of Mina's age to Naomi's age is . What is the three-way ratio of Lev's age to Mina's age to

geno3141 : However, if the ratios are not that nice: if you assume that the ratio of Lev's age to Mina's age is a / b and you assume that the ratio of Mina's age to Naomi's age is c / d, then: since a / b = a·c / b·c and c / d = b·c / c·d, the three-way ratio is: a·c : b·c : c·d.

You did the last part wrong. c / d = b·c / b·d So the three-way ratio is a·c: b·c: b·d

We need to know the ratios involved......

If you assume that the ratio of Lev's age to Mina's age is  L / M

and you assume that the ratio of Mina's age to Naomi's age is  M / N,

then the three-way ratio is:  L : M : N.

However, if the ratios are not that nice:

if you assume that the ratio of Lev's age to Mina's age is  a / b

and you assume that the ratio of Mina's age to Naomi's age is  c / d,

then:  since  a / b  =  a·c / b·c

            and  c / d  =  b·c / c·d,

the three-way ratio is:  a·c : b·c : c·d.

Yes Max, I get your answer too. :)