Ratio question

[Gobl0010]

So, if the number of 2nd graders to 4th graders is 8:5
and the number of 1st to 4th graders is 3:4
and the number of 3rd to 4th is 3:2

How do I determine the number of 1st to 3rd given the above

 

[rbcc]

I believe you can do iy like this

How do I determine the number of 1st to 3rd given the above

if the number of 2nd graders to 4th graders is 8:5 so \(\displaystyle \frac{2nd graders}{4th graders}=\frac{8}{5}\)

the number of 1st to 4th graders is 3:4 so \(\displaystyle \frac{1st graders}{4th graders}=\frac{3}{4}\)

the number of 3rd to 4th is 3:2 so \(\displaystyle \frac{3rd graders}{4th graders}=\frac{3}{2}\)

we want 1st to 3rd so \(\displaystyle \frac{1nd graders}{3rd graders}\)

so we multiple

\(\displaystyle \frac{1st}{4th}*\frac{4th}{3rd}\) the 4th will cancel out and we have 1st over 3rd
\(\displaystyle =\frac{3}{4}*\frac{2}{3}\)= 2/4 or 1/2