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

950−35w≤600

950+35w≥600

950−35w≥600
Question 2
(1 point)
Sam can continue spending money for
weeks.

1 answer

To find the correct inequality that represents the situation, we start with the initial amount Sam has, which is $950. He spends $35 each week, so after \( w \) weeks, the amount he has left can be represented as:

\[ 950 - 35w \]

Sam wants to have at least $600 left at the end of the summer, which gives us the inequality:

\[ 950 - 35w \geq 600 \]

Thus, the correct inequality to use is:

Answer: 950 - 35w ≥ 600


Now let's solve for the number of weeks (w) Sam can continue spending money.

  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 to flip the inequality sign): \[ w \leq 10 \]

Sam can continue spending for a maximum of 10 weeks.

Answer: 10 weeks.