The ratio of two numbers is 3: 5. when 4 is subtracted from the lesser of the two numbers and 8 is added to the larger of the two, the new ratio is 2: 7. what is the greater of the two numbers before 8 is added to it?

X and y
x:y=3:5
or
x/y=3/5

when 4 is subtracted from x and 8 is added to y new ratio is 2:7
(x-4)/(y+8)=2/7

we have
x/y=3/5
(x-4)/(y+8)=2/7

get rid o frationc

x/y=3/5
times both sides by 5y
5x=3y

(x-4)/(y+8)=2/7
times both sides by 7(y+8)
7(x-4)=2(y+8)
7x-28=2y+16
add 28 both sides
7x=44+2y

we have
5x=3y
and
7x=2y+44

multiply first equation by 2 and seecond equaiton by 3
10x=6y and 21x=6y+132

sub 10x for 6y
21x=10x+132
minus 10x both sides
11x=132
divide both sides by 11
x=12

x/y=3/5
12/y=3/5
times both sides by 5y
60=3y
divide both sid esyb 3
20=y

12 and 20

the greater is 20