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's assume the number of weeks Jake can continue giving away marbles is represented by the variable "w".
Every week, Jake gives away 100 marbles to friends. Therefore, the total number of marbles he should have 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. Therefore, we can write the inequality:
1000 - 100w ≥ 500
Simplifying the inequality, we get:
-100w ≥ -500
To solve for "w", we divide both sides of the inequality by -100 and reverse the direction of the inequality:
w ≤ -500 / -100
w ≤ 5
The solution to the inequality is w ≤ 5.
Therefore, Jake can continue giving away marbles for a maximum of 5 weeks, ensuring that he will have a minimum of 500 marbles left by the end of the summer.