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.
-
Start with the inequality: \[ 950 - 35w \geq 600 \]
-
Subtract 950 from both sides: \[ -35w \geq 600 - 950 \] \[ -35w \geq -350 \]
-
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.