A farmer planned to plant 120 seeds in all. After planting 10 more seeds each day than was planned, she was able to finish 2 days earlier. How many seeds were planted each day?

Let s=number of seeds and t=number of days ...

st=120 and (s+10) (t-2) = 120

From the first we can say t=120/s, now using this value of t in the second equation gives us:

(s+10) (120/s-2) = 120

(s+10) (120-2s) / s=120

(s+10) (120-2s) = 120s

120s-2s^2+1200-20s=120s

2s^2+20s-1200=0

s^2+10s-600=0

(s+30) (s-20) = 0, since s>0

s=20, and since she planted s+10 seeds per day to finish two days earlier:

20+10=30

She planted 30 seeds per day.