Sarah wants to buy a bicycle that costs at least $200. She has $80, and she earns $30 from her part-time job each week. Write an inequality for the number of weeks Sarah will need to save to have enough money to buy the bicycle, and describe the solutions. Note: Use x as the variable. You can write ≤ like this = * 1 point 30x + 80 ≥ 200 30x + 80 200 30x + 80

Question

Sarah wants to buy a bicycle that costs at least $200. She has $80, and she earns $30 from her part-time job each week. Write an inequality for the number of weeks Sarah will need to save to have enough money to buy the bicycle, and describe the solutions. Note: Use x as the variable. You can write ≤ like this <= You can write ≥ like this >= * 1 point 30x + 80 ≥ 200 30x + 80 > 200 30x + 80 < 200 30x + 80 ≤ 200 80x + 30 ≥ 200 80x + 30 ≤ 200 80x + 30 < 200 80x + 30 > 200

GPT-4o mini · Answer

To determine how many weeks Sarah will need to save to afford the bicycle that costs at least $200, we can set up the inequality based on her current savings and weekly earnings.

Sarah has $80 and earns $30 for each week she works. Therefore, we can represent the total amount of money she will have after $ x $ weeks with the following expression:

\[ 30x + 80 \]

We want this amount to be at least $200 to buy the bicycle. This scenario can be represented by the inequality:

\[ 30x + 80 \geq 200 \]

Now, let's describe the solutions.

To solve the inequality:

Subtract 80 from both sides: \[ 30x \geq 200 - 80 \] \[ 30x \geq 120 \]
Divide both sides by 30: \[ x \geq \frac{120}{30} \] \[ x \geq 4 \]

Explanation of the Solutions:

The solution $ x \geq 4 $ means that Sarah needs to save for at least 4 weeks to have enough money to purchase the bicycle. If she saves for 4 weeks or more, she will have enough funds to buy the bicycle costing at least $200.

So, the correct inequality is:

Answer: \[ 30x + 80 \geq 200 \]