Jake begins summer with 1,000marblee in his collection. He aims to have a minimum of 500 marbles left by the end of the summer. Each week, he gives away 108marbles to friends. Write an inequality to determine the number of weeks Jake can continue giving away marbles and find the solution.

Answer 1

Let's call the number of weeks that Jake can continue giving away marbles "w".

Since Jake gives away 108 marbles each week, the number of marbles he will have left after w weeks is given by 1000 - 108w.

He wants to have a minimum of 500 marbles left, so we can write the inequality as 1000 - 108w ≥ 500.

Now let's solve for w:
1000 - 108w ≥ 500
Subtract 1000 from both sides:
-108w ≥ -500
Divide both sides by -108 (remember to flip the inequality sign since we're dividing by a negative number):
w ≤ 500/108

Using long division, we find that 500/108 = 4.63.

Therefore, the solution is w ≤ 4.63. Since we can't have a fraction of a week, the maximum number of weeks Jake can continue giving away marbles is 4 weeks.