The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from the second day to the ninth day becomes 66. The number of copies sold on the first day of the book launch is:
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Correct Answer: 59
Approach Solution - 1
Let \(x_i\) represent the number of copies sold on the \(i\)th day, and let \(S_n\) denote the total number of copies sold in the first \(n\) days. Step 1: Use the given averages for the first 7 and 8 days. The average number of copies sold during the first 7 days is 60, so \[ S_7 = 7 \times 60 = 420. \] The average for the first 8 days is 63, hence \[ S_8 = 8 \times 63 = 504. \] Step 2: Determine the number of copies sold on the 8th day. \[ x_8 = S_8 - S_7 = 504 - 420 = 84. \] Step 3: Find the sales on the 9th day. It is given that on the 9th day, the sales were 11 fewer than on the 8th day. Therefore, \[ x_9 = x_8 - 11 = 84 - 11 = 73. \] Step 4: Use the average from the 2nd to the 9th day. From day 2 to day 9, there are 8 days, and the average number of copies sold is 66. Thus, \[ S_{2\text{--}9} = 8 \times 66 = 528. \] Step 5: Relate the totals to find the sales on the first day. The total number of copies sold in the first 9 days is \[ S_9 = S_8 + x_9 = 504 + 73 = 577. \] This total can also be expressed as \[ S_9 = x_1 + S_{2\text{--}9} = x_1 + 528. \] Equating the two expressions, \[ x_1 + 528 = 577 \Rightarrow x_1 = 49. \] Hence, the number of copies sold on the first day is \(49\).
Approach Solution -2
Step 2: Find the sales on the $8$th day. \[ x_8 = S_8 - S_7 = 504 - 420 = 84. \]
Step 3: Find the sales on the $9$th day. On the $9$th day, she sells $11$ copies less than on the $8$th day: \[ x_9 = x_8 - 11 = 84 - 11 = 73. \]
Step 4: Use the average from day $2$ to day $9$. From day $2$ to day $9$ there are $8$ days, and the average is $66$: \[ S_{2\text{--}9} = 8 \times 66 = 528. \]
Step 5: Relate totals to find $x_1$. Total sales in the first $9$ days: \[ S_9 = S_8 + x_9 = 504 + 73 = 577. \] But $S_9$ is also \[ S_9 = x_1 + S_{2\text{--}9} = x_1 + 528. \] So, \[ x_1 + 528 = 577 \;\Rightarrow\; x_1 = 577 - 528 = 49. \] Therefore, the number of copies sold on the first day is \(49\).
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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
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