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Question

Question
Sophie is eyeing a new bicycle that costs $1,200. She earns $160 per week from her part-time job. Currently, she has saved up $400. What inequality represents the minimum number of weeks (w) Sophie needs to work to afford the bicycle?(1 point)
Responses

400w+160w≥1200
400 w plus 160 w is greater than or equal to 1200

400+160w≥1200
400 plus 160 w is greater than or equal to 1200

400w+160w≤1200
400 w plus 160 w is less than or equal to 1200

400+160w≤1200
400 plus 160 w is less than or equal to 1200
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Answer 1

To determine the minimum number of weeks \( w \) Sophie needs to work in order to afford the bicycle, we can set up the inequality based on her savings and income.

1. She starts with $400 saved.
2. She earns $160 each week, which means in \( w \) weeks she will earn \( 160w \).
3. The total amount she will have after \( w \) weeks will be her initial savings plus her earnings:

\[ 400 + 160w \]

4. This total needs to be at least $1,200 in order for her to afford the bicycle:

\[ 400 + 160w \geq 1200 \]

Therefore, the correct inequality that represents the minimum number of weeks she needs to work is:

400 + 160w ≥ 1200

So, the correct response is: 400 + 160w ≥ 1200 (400 plus 160 w is greater than or equal to 1200).