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Catalog
Grades 11-12 Video Solutions 2024
2024_11-12_19
2024_11-12_19
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Video Transcription
Video Summary
The problem involves finding the sum of the digits of a four-digit number \( n \), represented as \( pqrs \). When a decimal is placed between \( q \) and \( r \), \( pq.rs \) becomes the average of the two-digit numbers \( pq \) and \( rs \). Setting \( a = pq \) and \( b = rs \), the equation \( a + 0.01b = \frac{a+b}{2} \) is used, leading to \( 50a = 49b \). Solving gives \( a = 49 \) and \( b = 50 \), making the number \( 4950 \). Thus, the sum of its digits is \( 4 + 9 + 5 + 0 = 18 \).
Keywords
digit sum
four-digit number
average
equation
4950
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