I have four numbers that total $1285$. The ratio of the first to second is $2:3$. The ratio of the second to third is $5:4$. The ratio of the third to fourth is $5:6$. Find the third number. So what did is set up this:
$a+b+c+d=1285$
$2a=3b$
$5b=4c$
$5c=6d$
Then:
$a=1.5b$
$b=0.8c$
$d=\frac{5c}{6} $
So:
$((1.5)*(0.8))c+(0.8)c+c+(5c/6)=1285$
Is this correct? And how would I take it from there? I also would like to know if there are other ways to do this. Thanks for all of your responses!
Another question that I had in solving this is that the question reads "the ratio of the first to second numbers is 2:3." To set that up, would it be 2a=3b or a/b=2/3, meaning 3a=2b? Thanks for your help.
Please note: I am aware that there is another very similar question on this site, but it did not yield an answer is now closed/on hold. If the other question is reopened, I will close this one. Thank you.
Note: This question has been answered on the other question. If you want an answer, you can get one at Original Ratios Problem
I like this method.
$\begin{bmatrix}2 & 3 & & \\ & 5 & 4 & \\ & & 5 &6 \end{bmatrix}$
$\begin{bmatrix}50 & 75 & & \\ & 75 & 60 & \\ & & 60 &72 \end{bmatrix}$
So we have the ratio as $50:75:60:72.$
Let the numbers be $50x, 75x, 60x, 72x.$
$x=\frac{1285}{227}=5$
The numbers are $250, 375, 300$, and $360$ that is, I hope.