Answer this 2 questions as much as possible please
Answers
Answer:
1) Two answers. The three numbers can be
2, 6, 10 OR 15, 6, -3.
2) He bought 16 books.
Step-by-step explanation:
1) Let a be the first number and let d be the common difference, so the first three numbers are a, a+d, a+2d.
Their sum = 18
=> a + a+d + a+2d = 18
=> 3a + 3d = 18
=> a + d = 6
=> d = 6 - a ... (1)
Product of first and third is 5 times the common difference
=> a ( a + 2d ) = 5d
=> a ( a + 2 ( 6 - a ) ) = 5 ( 6 - a ) [ using equation (1) ]
=> a ( a + 12 - 2a ) = 30 - 5a
=> a ( 12 - a ) = 30 - 5a
=> 12a - a² = 30 - 5a
=> a² - 17a + 30 = 0
=> ( a - 2 ) ( a - 15 ) = 0
=> a = 2 or a = 15.
If a = 2, then d = 6 - a = 4. The three numbers are then 2, 6, 10.
If a = 15, then d = 6 - a = -9. The three numbers are then 15, 6, -3.
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2) Let b be the number of books that he bought.
The cost per book is then 80/b.
If he bought 4 more for the same amount, the cost per book would be 80/(b+4). But we are told that this cost per book would be 1 less than before. So...
80 / ( b + 4 ) = 80 / b - 1
=> 80 / ( b + 4 ) = ( 80 - b ) / b
=> 80b = ( 80 - b ) ( b + 4 )
=> 80b = 80b + 320 - b² - 4b
=> b² + 4b - 320 = 0
=> ( b - 16 ) ( b + 20 ) = 0
=> b = 16 or b = -20.
As b cannot be negative, we conclude that b = 16.
So...
He bought 16 books.