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 his friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution.
Let x be the number of weeks Jake can continue giving away marbles.
The number of marbles Jake will have after giving away marbles for x weeks is given by:
1000 - 100x
According to the problem, Jake aims to have a minimum of 500 marbles left by the end of the summer. This can be represented by the inequality:
1000 - 100x >= 500
Simplifying the inequality, we get:
-100x >= 500 - 1000
-100x >= -500
Dividing both sides by -100 (and flipping the inequality sign because we're dividing by a negative number), we get:
x <= 5
Therefore, Jake can continue giving away marbles for a maximum of 5 weeks.