A university will spend at most $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250, and each keyboard will cost $50. Which inequality represents a... A university will spend at most $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250, and each keyboard will cost $50. Which inequality represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab?
Understand the Problem
The question is asking for an inequality that represents the financial constraints on purchasing monitors and keyboards for a university computer lab, based on their respective prices and a total budget. We need to determine how to mathematically express this relationship using variables for the quantities of monitors (x) and keyboards (y).
Answer
$50x + 250y \leq 4500$
Answer for screen readers
The correct inequality is $50x + 250y \leq 4500$.
Steps to Solve
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Identify the costs of items Each monitor costs $250 and each keyboard costs $50.
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Set up the inequality The university's total expenditure on monitors and keyboards cannot exceed $4,500. The spending can be described with the inequality: $$ 250x + 50y \leq 4500 $$
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Recognize the correct inequality format Since we're looking for inequalities that represent spending "at most" $4,500, we will use the "less than or equal to" symbol $\leq$.
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Choose the correct option From the given options, identify the expression that correctly matches our derived inequality.
The correct inequality is $50x + 250y \leq 4500$.
More Information
This inequality indicates that the total cost of monitors ($250$ per monitor) and keyboards ($50$ per keyboard) should not exceed the university's budget of $4,500. By rearranging terms, different forms of the inequality can be created, but they all reflect the same constraint.
Tips
- A common mistake is using the strict inequality ($<$) instead of the non-strict inequality ($\leq$) when a budget constraint "at most" is involved.
- Miscalculating the weights (costs) of items can also lead to incorrect formulations.
