Flashcard 2 - Math Flashcard Set for the SAT Exam

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It is given that the museum initially has 938 works in its collection and another 12 are to be added each year. The number of years, however, is subject to variation, so using the variable n to equal number of years, the expression \(938 + 12n\) represents how many works the museum will have after n years.

The problem is essentially asking how many years will pass before the museum reaches a minimum of 1500 works in its collection, which can be written mathematically as:

\[938 + 12n \ge 1500\]

Subtracting 938 from each side yields \(12n \ge 562\) and dividing both sides of this equation by 12 gives \(n \ge 46.83\) (approximately).

In this context, n needs to be a whole number and is therefore rounded up to 47, indicating that the museum will reach 1500 works 47 years after 2010, or in the year 2057.