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. Solve the inequality. Note: Make sure to write the inequality so the x comes first. You can write ≤ like this <= You can write ≥ like this >=

Answer 1

Let \( x \) be the number of weeks Sarah works at her part-time job. She currently has $80 and earns $30 each week, so after \( x \) weeks, her total amount of money will be:

\[ 80 + 30x \]

Since she wants to buy a bicycle that costs at least $200, we can set up the following inequality:

\[ 80 + 30x \geq 200 \]

Now, we will solve the inequality for \( x \):

1. Subtract 80 from both sides:

\[ 30x \geq 200 - 80 \] \[ 30x \geq 120 \]

2. Divide both sides by 30:

\[ x \geq \frac{120}{30} \] \[ x \geq 4 \]

Thus, the solution to the inequality is:

\[ 30x + 80 \geq 200 \]

or expressed in terms of \( x \):

\[ x \geq 4 \]

This means Sarah needs to work at least 4 weeks to afford the bicycle.