Algebra

A school district is ordering new Chromebooks for students. Each Chromebook costs $285. The district also has to pay a one-time shipping fee of $1,200. If the district has a budget of $30,000, what is the maximum number of Chromebooks they can purchase without going over budget?

Step-by-step solution with explanation

Final Answer

The district can purchase a maximum of **101 Chromebooks** for a total cost of 30,000 budget.

Step-by-step solution

1

Set up the inequality for budget

Let n be the number of Chromebooks. Each Chromebook costs 1,200 shipping fee. The total cost must stay at or below the $30,000 budget.
2

Subtract shipping fee from budget

We move the shipping fee to the right side by subtracting 1,200 from both sides. This tells us how much money is left for the actual Chromebooks.
3

Simplify the right side

30,000 minus 1,200 equals 28,800. So the district has $28,800 left to spend on Chromebooks after paying shipping.
4

Divide both sides by 285

Dividing both sides by 285 isolates n. This gives us approximately 101.05, which is the maximum value of n before going over budget.
5

Round down to a whole number

You can't buy a fraction of a Chromebook, so we round DOWN to 101. Rounding up to 102 would go over budget, so we must take the floor of 101.05.
6

Verify the answer is within budget

Plugging 101 back in gives a total cost of 15 under the $30,000 budget. This confirms 101 is correct.

Understanding this problem

Learning Insight

This is a linear inequality problem. The key idea is that real-world problems involving whole objects (like Chromebooks) require you to take the floor of your answer — even if the math gives a decimal, you can only buy complete items. Always check your rounded answer by plugging it back in.

Quick Tip

After dividing, always ask: 'Is my answer a whole number?' If not, round DOWN for a maximum quantity problem and round UP for a minimum quantity problem. Never round the usual way.

Common Mistake

Students often round 101.05 up to 102 using standard rounding rules. But buying 102 Chromebooks costs 1,200 = $30,270, which exceeds the budget. Always round DOWN when finding a maximum quantity.