The ratio of two positive numbers is 3 to 4. if k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. what is the value of k

Let the two numbers be x and y

x/y=3/4

Therefore x=3z

y=4z, where z is the GCF of x and y

(3z+k) / (4z+k) = 4/5

(3z+k) * 5 = (4z+k) * 4

15z+5k=16z+4k

k=z--->eq1

3z+k+4z+k=117

7z+2k=117--->eq2

Using value of z from eq1 in eq2

7k+2k=117

k=117/9

=13