Question

Ratio question : The ratio of the ages of Anna and Emma is 3:5 and the ratio of the ages of Emma and Nicholas is 3:5 . What is the ratio of Anna's age to Nicholas age? I have no idea how to deal with this type of question.

Answer 1

Anna age = A
Emma age = E
Nicholas age = N

If Anna/Emma = 3/5 , you can say that Anna age is 3K and Emma age is 5K (K a constant).

Ok, Emma / Nicholas = 3/5, change Emma to 5K and Nicholas to N.

5K/N = 3/5
25K = 3N
N = 25K/3

You want the ratio of Anna and Nicholas. If Anna = 3K and Nicholas = 25K/3, the ratio is :
3K / (25K/3) = 9/25

Answer 2

Thank you!, that was a great answer , I still have trouble getting the logic behind it . I will have to do more of these problems

Answer 3

There are others ways to solve this, you can solve without using the constant k, but for me it's more difficulty. Wanna see that?

Answer 4

Again,
Anna age = A
Emma age = E
Nicholas age = N

\[\frac{ A }{ E } = \frac{ 3 }{ 5 }\]\[5A=3E\]\[E = \frac{ 5A }{ 3 }\].

Ok, and
\[\frac{ E }{ N } = \frac{ 3 }{ 5 }\]
\[5E=3N\]

Change \[E \to \frac{ 5A }{ 3 }\] You will have:
\[5*(\frac{ 5A }{ 3 }) = 3N\]\[\frac{ 25A }{ 3 }=3N\]\[25A=9N\]\[\frac{ A }{ N }=\frac{ 9 }{ 25 }\]

Answer 5

oh wow , I actually got this explanation better. Thanks a lot!!!