A postal employee delivered mail daily for 42 days, each day delivering 4 more
letters than the day before. The total delivery for the first 24 days of the period was
the same as that for the last 18 days. How many letters did the employee deliver
during the whole 42 day period?
Answers
Given : A postal employee delivered mail daily for 42 days, each day delivering 4 more letters than the day before. The total delivery for the first 24 days of the period was the same as that for the last 18 days
To find : How many letters did the employee deliver during the whole 42 day period
Solution:
Let say Delivered on first day = a
each day delivering 4 more letters than the day before
=> d = 4
Sum of an AP = (n/2)(2a + (n-1)d)
Delivered in 1st 24 days
= (24/2) (2 * a + (24 - 1) 4)
= 12(2a + 92)
= 24 (a + 46)
Delivered in last 18 days
=> 25th to 42 days
25th day = a + 24d = a + 24(4) = a + 96
Delivered in last 18 days
= (18/2) (2 (a + 96) + (18 - 1) 4)
= 9 ( 2a + 192 + 68)
= 9 (2a + 260)
= 18(a + 130)
24 (a + 46) = 18(a + 130)
=> 4 (a + 46) = 3(a + 130)
=> 4a + 184 = 3a + 390
=> a = 206
a = 206 d = 4
n = 42
Sum = (42/2) ( 2 * 206 + (42 - 1) 4)
= 21 ( 412 + 164)
= 21 ( 576)
= 12096
Employee delivered 12096 letter during the whole 42 days
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