The sum of two numbers is 120. four times the larger divided by twice the smaller is thirty-four.

Let the numbers be a and b.

The sum of the numbers is 120, so we have: i) a+b=120

Four times the larger divided by twice the smaller is thirty-four:

assume the larger is a :  

ii)  


substitute a=17b in the first equation:

a+b=120

17b+b=120

18b=120

b=120/18=60/9=20/3

thus, a=17b=17(20/3)=340/3

 20/3, 340/3