am 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.

Question

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 minus 35 w is less than or equal to 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.

Answer 1

To solve the problem, we need to express the situation involving Sam's spending and the minimum amount he wants to have left.

1. Sam starts with $950, and he is spending $35 each week. The amount he has after \( w \) weeks is given by the expression:

   \[ 950 - 35w \]

2. Sam wants to have at least $600 left by the end of the summer. This gives us the following inequality:

   \[ 950 - 35w \geq 600 \]

So the correct inequality to determine the number of weeks (w) Sam can continue spending money is:

950 - 35w ≥ 600

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For Question 2, we will solve the inequality:

1. Start with the inequality:

   \[ 950 - 35w \geq 600 \]

2. Subtract 950 from both sides:

   \[ -35w \geq 600 - 950 \]

   \[ -35w \geq -350 \]

3. Divide both sides by -35 (remember that dividing or multiplying by a negative number reverses the inequality):

   \[ w \leq 10 \]

Thus, Sam can continue spending money for 10 weeks.