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Question

Question 1
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.

Which inequality should be used to determine the number of weeks (w) Sam can continue spending money?

(1 point)
Responses

950+35w>600
950 plus 35 w is greater than 600

950−35w ≤600
950−35w ≤600

950+35w≥600
950 plus 35 w is greater than or equal to 600

950−35w≥600
950 minus 35 w is greater than or equal to 600
Question 2
(1 point)
Sam can continue spending money for
weeks.
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Answer 1

To determine the correct inequality for the problem, let's analyze it step by step.

1. Sam starts with $950.
2. He wants to have at least $600 left at the end of summer, which means he can spend up to $950 - $600 = $350.
3. 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 \( w \):

1. Subtract 950 from both sides: \[ -35w \geq 600 - 950 \] \[ -35w \geq -350 \]

2. Divide by -35 (note that the inequality sign flips): \[ w \leq 10 \]

So, Sam can continue spending money for a maximum of 10 weeks.