The sum of two numbers is 200 and the two numbers are in a ratio of 4: 6 find the larger number

Let x be the 1st number an y, the 2nd:

a) x+y = 200
b) x/y = 4/6

Remember that if we have a/b = c/d, we can write (a+b)/b = (c+d)/d
So if x/y = 4/6, then (x+y)/y = (4+6)/6
But x+y = 200, then:
200/y = 10/6 
Cross multiplication→ 10y = 1200 and y = 120 and x= 200-120 and x = 80.
Proof:
x/y = 80/120 = 8/12 = 4/6