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.

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.
A. w > 86
B. w > 8.6
C. w > 51.2
D. w > 860

GPT 3.5 · Answer

To solve the inequality 10w + 213 > 299, we first need to isolate w.

Subtract 213 from both sides:
10w + 213 - 213 > 299 - 213
10w > 86

Divide by 10:
w > 8.6

Therefore, Ellie will have enough money saved after more than 8.6 weeks. Since a partial week doesn't make sense, we can round up to the nearest whole number, so Ellie will have enough money saved after 9 weeks. This matches option B: w > 8.6.