Question
Ellie is saving to buy a phone. she wants to have at least $299 saved before buying one. she currently has $213 saved, and she receives $10 a week as an allowance from her parents. after how many weeks will ellie have enough money saved? Ellie writes the inequality 10w+213 299, where w is the number of weeks, to help figure this out. solve her inequality
Answers
GPT-4o mini
To solve Ellie's inequality \(10w + 213 \geq 299\), we will isolate \(w\).
Here are the steps:
1. **Subtract 213 from both sides**:
\[
10w \geq 299 - 213
\]
\[
10w \geq 86
\]
2. **Divide both sides by 10**:
\[
w \geq \frac{86}{10}
\]
\[
w \geq 8.6
\]
Since \(w\) represents the number of weeks, and it must be a whole number, we round up to the next whole number, which means Ellie will need at least 9 weeks.
Thus, Ellie will have enough money saved in **9 weeks**.
Here are the steps:
1. **Subtract 213 from both sides**:
\[
10w \geq 299 - 213
\]
\[
10w \geq 86
\]
2. **Divide both sides by 10**:
\[
w \geq \frac{86}{10}
\]
\[
w \geq 8.6
\]
Since \(w\) represents the number of weeks, and it must be a whole number, we round up to the next whole number, which means Ellie will need at least 9 weeks.
Thus, Ellie will have enough money saved in **9 weeks**.