Roy is 96 years younger than Rachel 6 years ago Rachel's age was four times Roy's age how old is Roy now

Why do they have to have names starting with same letter

x=roy's age now

y=rachel's age now

roy is 96 years younger than rachel

x=y-96

6 years ago (x-6 and y-6), rachel's age was 4 times roy's age

so

y-6=4 (x-6)

so

x=y-96 and

y-6=4 (x-6)

use x=y-96

add 96 both sides

x+96=y

subsiute x+96 for y in other equation

y-6=4 (x-6)

x+96-6=4 (x-6)

x+90=4 (x-6)

distribute

x+90=4x-24

add 24 to both sides

x+114=4x

minus x both sides

114=3x

divide both sides by 3

38=x

x=38

roy is 38 years old now