Sam starts the summer with $950 in his wallet. He aims to have a minimum of $600 left by the end of the summer. Each week, he spends $35 on recreational activities. Write an inequality to determine the number of weeks Sam can continue spending money, and solve the inequality.
Let x be the number of weeks Sam can continue spending money.
His total spending on recreational activities is $35 * x.
His total money left is $950 - $35 * x.
According to the problem, $950 - $35 * x must be greater than or equal to $600.
Therefore, the inequality is:
$950 - $35 * x ≥ $600.
To solve the inequality, we can subtract $950 from both sides to get:
-$35 * x ≥ -$350.
Then, we divide both sides by -$35. Since we are dividing by a negative number, the inequality changes direction.
x ≤ -$350 / -$35.
x ≤ 10.
Sam can continue spending money for a maximum of 10 weeks. Answer: \boxed{10}.