Tom performed a total of 100 hours of community service. He served at three charities - Salvation Army, Red Cross and Rescue Missiom. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross

Let x, y, z be the number of hours that Tom spent in service in Salvation Army, Red Cross, and Rescue Mission, respectively. From the statement above, the sum of the numbers should be 100.

x + y + z = 100

The equations that can be derived from the given and the assigned variables,

y = x + 19

z = y + 8

Expressing the times in terms of variable x,

y = x + 19

z = (x + 19) + 8 = x + 27

Solving for the value of x,

x + (x + 19) + (x + 27) = 100

The value of x from the equation is 18.

y = 18 + 19 = 37

z = 18 + 27 = 45

The number of hours he spent in three charities are 18, 37, and 45, respectively.