let

j = the number of runs Jim scored

n = the number of runs Norman scored

d = the number of runs Dennis scored

p = the number of runs Pete scored

In their last match Jim scored 15 more runs than Norman,

j = 15 + n

Dennis scored 5 times as many as Norman

d = 5n

and sixteen more than Pete

d = 16 + p

p = d - 16

p = 5n - 16 (since d = 5n)

In total they scored 107 runs:

j +n + d + p = 107

plug j = 15 + n, d = 5n and p = 5n - 16 into the last equation:

15 + n + n + 5n + 5n - 16 = 107

by solving we find:

n = 9 runs

click here to see the step by step solution of the equation:

j = 15 + 9 = 24 runs

d = 5n = 5*9 = 45 runs

p = 5n - 16 = 5*9 - 16 = 29 runs

Jim scored 24 runs.

Norman scored 9 runs.

Denis scored 45 runs.

Pete scored 29 runs.