A grocer dresses his shop window with sunlight bar soaps, placing 30 in the first row, 29 in the second, 28 in the third, and so on. If there are 387 bars soaps in all, how many rows are there, and how many in the topmost row.
Answers
Given : A grocer dresses his shop window with sunlight bar soaps, placing 30 in the first row, 29 in the second, 28 in the third, and so on.
there are 387 bars soaps in all
To Find : how many rows are there, and how many in the topmost row.
Solution:
Let say there are n rows
this is an AP
30 , 29 , 28 ,,,,,,,,,,,,,,,,,,,,,,,
a = 30
d = - 1
Last row = a + (n-1)d = 30 + (n-1)(-1) = 31 - n
Sum = (n/2)(30 + 31 - n)
= (n/2)(61 - n) = 387
=> 61n - n² = 774
=> n² - 18 n - 43n + 774 = 0
=>(n - 18)(n-43) = 0
=> n = 18 , n = 43
n = 43 not possible as maximum can be 30
n = 18
Rows = 18
Last row = 31 - 18 = 13
topmost row. = 13
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