Jake begins the summer with 1,000 marbles in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 100 marbles to friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution
A. 1000-100w ≥ 500; w ≥ 5
B. 1000-100w ≥ 500; w ≤ 5
C. 1000-100w ≤ 500; w ≥ 6
D. 1000+100w ≥500; w ≥ 6
To determine the number of weeks Jake can continue giving away marbles, we need to find the number of weeks (w) that satisfies the inequality.
Since Jake gives away 100 marbles each week, the number of marbles he has after w weeks is given by 1000 - 100w.
To have a minimum of 500 marbles left, we set up the inequality:
1000 - 100w ≥ 500
Simplifying this inequality gives us:
-100w ≥ -500
Dividing both sides of the inequality by -100 (and flipping the inequality sign) gives us:
w ≤ 5
Therefore, the inequality that represents the number of weeks Jake can continue giving away marbles is 1000 - 100w ≥ 500, and the solution is w ≤ 5.
The correct answer is B. 1000-100w ≥ 500; w ≤ 5