1. **State the problem:** We need to find the cost per tree for two types of Christmas trees: Noble Fir (n) and Douglas Fir (d). 2. **Write the system of equations from the problem:** $$5n + 3d = 420$$ $$12n + 9d = 1080$$ 3. **Simplify the second equation by dividing all terms by 3:** $$\cancel{12}n + \cancel{9}d = \cancel{1080}$$ $$4n + 3d = 360$$ 4. **Subtract the first equation from the simplified second equation to eliminate $d$:** $$(4n + 3d) - (5n + 3d) = 360 - 420$$ $$4n + 3d - 5n - 3d = -60$$ $$-n = -60$$ 5. **Solve for $n$:** $$n = 60$$ 6. **Substitute $n=60$ into the first equation to find $d$:** $$5(60) + 3d = 420$$ $$300 + 3d = 420$$ 7. **Isolate $d$:** $$3d = 420 - 300$$ $$3d = 120$$ 8. **Solve for $d$:** $$d = \frac{120}{3}$$ $$d = 40$$ **Final answer:** - Cost of Noble Fir tree $n = 60$ - Cost of Douglas Fir tree $d = 40$