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
Explanation:
The inequality represents the amount of money Sam will have left after spending $35 per week for w number of weeks.
Since Sam starts with $950 and spends $35 each week, the amount of money he will have left after w weeks is 950 - 35w.
According to the problem, Sam wants to have a minimum of $600 left at the end of the summer. Hence, the inequality can be written as 950 - 35w ≥ 600.
To solve the inequality, isolate the variable w by subtracting 950 from both sides:
950 - 35w - 950 ≥ 600 - 950
-35w ≥ -350
Divide both sides of the inequality by -35, but remember to reverse the inequality sign because we are dividing by a negative number:
w ≤ -350 / -35
w ≤ 10
So, the solution to the inequality is w ≤ 10, meaning Sam can continue spending money for a maximum of 10 weeks.