Divide $32,175 between Sean and Rae in the ratio 8:5

8:5 this is read 8 to 5 and means 8 parts to 5 parts that said how many parts are there??
add them up 8+5 = 13 so dude gets 8/13 and chick gets 5/13.
for dude
32175(8/13)= 257400/13= $19,800 <-- Sean's cash
for chick
32175(5/13)= 160875/12= $12,375 <-- Rae's money

first check add up your answers
$19,800+$12,375=$32175 <-- this is good...

use the calculator to check the ratio

19,800/12,375 = 1.6 = 16/10 = 8/5 <-- so i know its right.

Cheers!
A.

Sean gets 8 parts and Rae gets 5 parts. That's 13 parts in total.
So we divide total amount by 13, then multiply by 8 for Sean, and 5 for Rae

$32,175/13 = $2,475

Sean: 8 * $2,475 = $19,800
Rae: 5 * $2,475 = $12,375

8+5=13
Divide 32175 by 13=2475
Sean wants 8 parts so (8x2475=19800)
Rae wants 5 parts so (5x2475=12375)

I know it's not in an equation but this is how i would solve it without pen and paper

x+y = 32175
x/y = 8/5
x/(x+y) = 8/13
x = 8/13*32175 = 19800
y = 5/13*32175 = 12375