To solve this system of equations, we can use the method of substitution.

From the first equation, we have x/7 = y/4 = z/3.

Let's solve for x in terms of y using the first equation:
x/7 = y/4
Cross multiplying, we get:
4x = 7y
x = (7y)/4

Now, let's solve for z in terms of y using the first equation:
z/3 = y/4
Cross multiplying, we get:
4z = 3y
z = (3y)/4

Substituting these expressions for x and z into the second equation:
x - 3y + 3z = 24
((7y)/4) - 3y + 3((3y)/4) = 24
Multiplying through by 4 to eliminate the fractions:
7y - 12y + 9y = 96
4y = 96
y = 24

Now that we have the value of y, we can substitute it back into the expressions for x and z to find their values:
x = (7y)/4 = (7(24))/4 = 42
z = (3y)/4 = (3(24))/4 = 18

Therefore, the solution to the system of equations is x = 42, y = 24, and z = 18.