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.
Let w represent the number of weeks. The number of marbles Jake will have after w weeks can be represented by the inequality:
1000 - 100w ≥ 500
To find the solution, solve the inequality for w:
1000 - 100w ≥ 500
-100w ≥ 500 - 1000
-100w ≥ -500
w ≤ (-500)/(-100)
w ≤ 5
The solution is w ≤ 5. Therefore, Jake can continue giving away marbles for a maximum of 5 weeks.