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.
A. 950+ 35w > 600; w ≥ 11
B. 950 - 35w ≥ 500; w ≤ 11
C. 950 + 35w ≥ 600; w ≥ 10
D. 950 - 35w ≥ 600; w ≤ 10
The correct answer is D. 950 - 35w ≥ 600; w ≤ 10.
To solve the inequality, we can subtract 600 from both sides of the inequality:
950 - 600 - 35w ≥ 600 - 600
350 - 35w ≥ 0
Then, we can subtract 350 from both sides:
350 - 35w - 350 ≥ 0 - 350
-35w ≥ -350
Finally, divide both sides of the inequality by -35 (remembering to reverse the inequality symbol when dividing by a negative number):
-35w / -35 ≤ -350 / -35
w ≤ 10
Therefore, the solution to the inequality is w ≤ 10. This means that Sam can spend money for a maximum of 10 weeks and still have at least $600 left by the end of the summer.