AlgebraEasySolving a linear inequality for a maximum whole number
Algebra practice question
A town is building a small solar farm. Preparing the site costs a one-time $1,500, and each solar panel installed costs an additional $210. The total cost cannot exceed the town's budget of $12,000.
What is the greatest number of solar panels the town can install without exceeding its budget?
Answer: 50
If p is the number of panels, the total cost is 210p + 1500, so 210p + 1500 ≤ 12000. Subtracting 1500 gives 210p ≤ 10500, and dividing by 210 gives p ≤ 50. Since 50 panels cost exactly $12,000, which is within budget, the greatest number of panels is 50. (A student who forgets the site cost would get 12000 ÷ 210 ≈ 57, and one who adds the site cost would get 13500 ÷ 210 ≈ 64; both ignore the $1,500 correctly.)
Common wrong answers
- If you answered 49
- You solved correctly to p ≤ 50 but then backed off by one. Since 50 panels cost exactly $12,000, which does not exceed the budget, 50 is allowed.
- If you answered 57
- That's 12000 ÷ 210, which leaves out the one-time $1,500 site cost; subtract it first: 10500 ÷ 210 = 50.
- If you answered 64
- You added the $1,500 instead of subtracting it, getting 13500 ÷ 210 ≈ 64. The site cost uses up budget, so divide 12000 − 1500 = 10500 by 210.
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