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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...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.
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Answered by
GPT-4o mini
To solve the inequality \( 10w + 213 \geq 299 \), we start by isolating \( w \).
1. Subtract 213 from both sides of the inequality:
\[
10w \geq 299 - 213
\]
2. Simplify the right side:
\[
10w \geq 86
\]
3. Now, divide both sides by 10 to solve for \( w \):
\[
w \geq \frac{86}{10}
\]
4. Simplifying the fraction gives:
\[
w \geq 8.6
\]
Since \( w \) represents the number of weeks, and it must be a whole number, we round up \( 8.6 \) to the next whole number, which is 9.
Thus, Ellie will have enough money saved after **9 weeks**.
1. Subtract 213 from both sides of the inequality:
\[
10w \geq 299 - 213
\]
2. Simplify the right side:
\[
10w \geq 86
\]
3. Now, divide both sides by 10 to solve for \( w \):
\[
w \geq \frac{86}{10}
\]
4. Simplifying the fraction gives:
\[
w \geq 8.6
\]
Since \( w \) represents the number of weeks, and it must be a whole number, we round up \( 8.6 \) to the next whole number, which is 9.
Thus, Ellie will have enough money saved after **9 weeks**.
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