There are 91 problems in the new math textbook. Paul started solving them in the mornings from September 7th. Starting September 8, he solves one problem less than the previous morning, until the problems are over. On the evening of September 9, Paul realized that there were still 46 unsolved problems in the textbook. What September does he complete all the problems in the textbook?​

Radarfoto67 2022-09-14 Answered
There are 91 problems in the new math textbook. Paul started solving them in the mornings from September 7th. Starting September 8, he solves one problem less than the previous morning, until the problems are over. On the evening of September 9, Paul realized that there were still 46 unsolved problems in the textbook. What September does he complete all the problems in the textbook?​
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Answers (1)

Karla Bautista
Answered 2022-09-15 Author has 16 answers
On September 7, Paul solved X problems, on September 8 - (X - 1), on September 9 - (X - 2).
Paul solved X + (X - 1 ) + (X - 2 ) = 3X - 3 = 91 - 46 = 45 problems in three days.
Х = 16 problems - Paul solved on September 7, (Х - 1 ) = 15 problems - Paul solved on September 8, ( Х - 2 ) = 14 problems - Paul solved on September 9.
On September 10, Paul will solve 14 - 1 = 13 problems and there will be 46 - 13 = 33 problems left to solve.
On September 11, Paul will solve 13 - 1 = 12 problems and there will be 33 - 12 = 21 problems left to solve.
On September 12, Paul will solve 12 - 1 = 11 problems and there will be 21 - 11 = 10 problems to solve.
On September 13, Paul will solve 11 - 1 = 10 problems and there will be 10 - 11 = 0 problems to solve - all problems are solved.
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