A3 If the members of the ski club pay 100 euros for the annual membership, they get a $50\%$ discount on the purchase of a daily ski pass. If they pay 200 euros for the annual membership, they get an $80\%$ discount on the purchase of a daily ski pass. A daily pass costs 30 euros. For how many days at least per year would they need to ski for it to be more advantageous to pay the more expensive membership?
(A) 50
(B) 12
(C) 18
(D) 20
(E) 15
A3. If we pay 200 euros for membership, the price of a ski pass is 6 euros. If we pay 100 euros for membership, the price of a ski pass is 15 euros. We conclude that the purchase is worthwhile if $100+x \cdot 15>$ $200+x \cdot 6$. We rearrange the inequality to $9 x>100$ and solve for $x>11 \frac{1}{9}$. We conclude that the purchase is worthwhile if we ski at least 12 days.