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.
1. 1000 - 100w ≥ 500; w ≥ 5
2. 1000 − 100w ≥ 500; w ≤ 5
3.1000 − 100w ≤ 500; w ≥ 6
4.1000 + 100w ≥ 500; w ≥ 6
The correct inequality is: 1000 - 100w ≥ 500.
This means that Jake must have at least 500 marbles left (represented by the 500 on the right side of the inequality) after giving away a certain number of marbles each week (represented by the 100w on the left side of the inequality).
To find the solution, we solve the inequality for w (the number of weeks):
1000 - 100w ≥ 500
-100w ≥ -500
w ≤ 5
So the solution is that Jake can continue giving away marbles for a maximum of 5 weeks.