To determine the correct inequality for the problem, let's analyze it step by step.
- Sam starts with $950.
- He wants to have at least $600 left at the end of summer, which means he can spend up to $950 - $600 = $350.
- Each week, Sam spends $35 on recreational activities.
We can set up the inequality based on what he can spend:
- The total amount spent after \( w \) weeks will be \( 35w \).
- The amount he has left after spending that money is \( 950 - 35w \).
To find out how long he can spend without going below $600, we want to ensure that:
\[ 950 - 35w \geq 600 \]
This means he can spend until the amount left is greater than or equal to $600.
Thus, the correct inequality is:
950 − 35w ≥ 600
Now for Question 2, we can solve this inequality for \( w \):
-
Subtract 950 from both sides: \[ -35w \geq 600 - 950 \] \[ -35w \geq -350 \]
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Divide by -35 (note that the inequality sign flips): \[ w \leq 10 \]
So, Sam can continue spending money for a maximum of 10 weeks.