Jake begins the summer with 1000 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 written inequality to determine the number of weeks. Jake can continue giving away marbles and find the solution.
Let's assume that Jake gives away 100 marbles each week after the summer begins.
Let's use "w" to represent the number of weeks that have passed.
Since Jake began with 1000 marbles and gives away 100 marbles each week, the number of marbles remaining after "w" weeks is 1000 - 100w.
According to the problem, Jake aims to have a minimum of 500 marbles left by the end of the summer. So, we can write the inequality:
1000 - 100w ≥ 500
Simplifying the inequality, we get:
-100w ≥ 500 - 1000
-100w ≥ -500
Dividing both sides of the inequality by -100 (and flipping the inequality sign since we're dividing by a negative number), we get:
w ≤ -500 / -100
w ≤ 5
Therefore, the number of weeks, "w", should be less than or equal to 5 in order for Jake to have a minimum of 500 marbles left by the end of the summer.