Question

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?

Answer 1

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.