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According to an autograph association, only 5% of autographs in circulation from a certain band are estimated to be real. If there are 77 authentic autographs of the band in circulation, then how many nonauthentic autographs are there in circulation? There are ◻ nonauthentic autographs in circulation. (Round to the nearest integer as needed.)

According to an autograph association, only 5% 5 \% of autographs in circulation from a certain band are estimated to be real. If there are 7777 authentic autographs of the band in circulation, then how many nonauthentic autographs are there in circulation?\newlineThere are □ \square nonauthentic autographs in circulation.\newline(Round to the nearest integer as needed.)

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Q. According to an autograph association, only 5% 5 \% of autographs in circulation from a certain band are estimated to be real. If there are 7777 authentic autographs of the band in circulation, then how many nonauthentic autographs are there in circulation?\newlineThere are □ \square nonauthentic autographs in circulation.\newline(Round to the nearest integer as needed.)
  1. Understand the problem: Understand the problem and what is given.\newlineWe know that 5%5\% of the autographs are real, and there are 7777 authentic autographs in circulation. We need to find the total number of autographs in circulation to then determine the number of nonauthentic autographs.
  2. Calculate total autographs: Calculate the total number of autographs in circulation.\newlineSince 5%5\% are real and we have 7777 real autographs, we can set up the equation:\newline0.05×Total number of autographs=770.05 \times \text{Total number of autographs} = 77\newlineTotal number of autographs=770.05\text{Total number of autographs} = \frac{77}{0.05}\newlineTotal number of autographs=1540\text{Total number of autographs} = 1540
  3. Calculate nonauthentic autographs: Calculate the number of nonauthentic autographs.\newlineNow that we know the total number of autographs, we can find the number of nonauthentic autographs by subtracting the number of authentic autographs from the total number.\newlineNumber of nonauthentic autographs == Total number of autographs −- Number of authentic autographs\newlineNumber of nonauthentic autographs =1540−77= 1540 - 77\newlineNumber of nonauthentic autographs =1463= 1463

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