Because c = 3d - 27, we can replace "c" with "3d - 27"
So in the equation 4d + 10c = 120 we can replace c (as stated above)
to get the equation 4d + 10(3d - 27) = 120
Now we have an equation with one variable and can solve for d.
4d + 10(3d - 27) = 120 [distribute]
4d + 30d - 270 = 120 [combine like terms]
34d - 270 = 120 [add 270]
34d = 390 [divide by 34]
d = 390/34 [simplify]
d = 195/17
Now to solve for c, pick either original equation, plug in the value of d, and solve for c. (The one where c is isolated is easier to use.)
c = 3d - 27
c = 3(195/17) - 27
c = 585/17 - 27
c = 585/17 - 459/17
c = 126/17