Sam starts the summer with $950 in his wallet. He aims to have a minimum of $600 left by the end of the summer. Each week, he spends $35 on recreational activities. Write an inequality to determine the number of weeks Sam can continue spending money, and solve the inequality.
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Let's say the number of weeks Sam can continue spending money is represented by "x".
Since Sam spends $35 per week, the total amount of money he will spend on recreational activities after "x" weeks is 35 * x.
The amount of money Sam has left after "x" weeks is $950 - (35 * x).
We want to find the number of weeks "x" such that Sam has at least $600 left, so the inequality is:
$950 - (35 * x) ≥ $600
Simplifying the inequality, we have:
950 - 35x ≥ 600
Adding 35x to both sides:
950 ≥ 600 + 35x
Subtracting 600 from both sides:
350 ≥ 35x
Dividing both sides by 35:
10 ≥ x
So Sam can continue spending money for a maximum of 10 weeks.
Can you write an inequility for that
Certainly!
The inequality would be:
950 - 35x ≥ 600
This inequality states that the difference between the initial amount of money Sam has ($950) and the amount of money he spends on recreational activities after "x" weeks (35x) should be greater than or equal to the minimum amount of money he wants to have left ($600).