The ratio of incomes of two persons is 9: 7. the difference in their weekly income is $200. what are their weekly incomes?

X= person 1
y= person 2

Their ratio is 9/7, so x/y is also true:
x/y=9/7

Let's solve for x:
x/y=9/7
Multiply both sides by the reciprocal of 1/y to get rid if y as a denominator

(y/1)(x/y)= (9/7)(y/1)
x= (9*y)/7
x= 9y/7

The difference in their incomes will be a subtraction problem

x-y=200
Substitute the answer for x in this equation to find how much person x makes.
(9y/7)-y= 200
Multiply everything by 7 to eliminate the 7 denominator
(7)(9y/7)-(7)(y)=(7)(200)
9y-7y=1400
2y= 1400
Divide both sides by 2
y= $700 person 2's weekly income

Substitute person 2's $ amount into the equation to find person 1's income
x-y=200
x-700=200
Add 700 to both sides
x= $900 person 1's weekly income

Hope this helped :)