Pre-Algebra Question of the Day

1. $b \geq 8$, so the minimum is 8 boxes
2. $b \geq 12$, so the minimum is 12 boxes
3. $b \geq 0$, so the minimum is 0 boxes
4. $b \geq 4$, so the minimum is 4 boxes (correct answer)

Explanation: When you encounter inequality word problems, start by understanding what the inequality represents and then solve it step by step to find what the variable must satisfy. Let's solve the inequality $15(8 + b) \geq 180$. First, divide both sides by 15: $8 + b \geq 12$. Then subtract 8 from both sides: $b \geq 4$. This means the bakery needs at least 4 additional boxes beyond the 8 they already filled. Let's verify: With 4 additional boxes, they'd have $8 + 4 = 12$ total boxes, containing $15 \times 12 = 180$ cupcakes, which exactly meets their requirement. Since they need "at least" 180 cupcakes, 4 additional boxes is the minimum. Choice A incorrectly states $b \geq 8$, which would mean they need 8 additional boxes on top of the 8 already filled—that's 16 total boxes for 240 cupcakes, way more than necessary. Choice B claims $b \geq 12$, suggesting 12 additional boxes for 20 total boxes and 300 cupcakes—again, excessive. Choice C states $b \geq 0$, which would mean no additional boxes are needed, but 8 boxes only hold 120 cupcakes, falling short of the 180 requirement. When solving inequality word problems, always substitute your answer back into the original context to verify it makes sense. Here, 4 additional boxes gives exactly 180 cupcakes, confirming this is indeed the minimum needed to satisfy "at least 180."