The sum of two numbers is 68. five times the smaller number is 16 more than the larger. find the two numbers.

We can use simultaneous equations to solve that. Which means we can solve 2 unknown numbers from 2 algebraic formulas.

Let the smaller number be y, and the larger number be z.

Now list the 2 equations from the given info.

y + z = 68 (equation 1)
5y = 16 + z (equation 2)

From (1),
y = 68 - z (equation 3)

Substitute (3) into (2).
5 (68-z) = 16 + z
340 - 5z = 16 + z
324 = 6z
z = 54

Now substitute z = 54 back into (1).
y + 54 = 68
y = 14

Therfore the 2 numbers are 14 and 54