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26 Mar 2025, 00:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:22) correct
34%
(02:18)
wrong
based on 125
sessions
History
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Time
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Sales of shovels have steadily declined at Al’s House of Garden Implements; each day Al’s sells one fewer shovel than it sold the previous day. Al’s is open seven days a week, and sold 329 shovels during the first week in March. How many shovels will Al’s sell during the second week in March if the trend continues?
A. 280
B. 287
C. 294
D. 308
E. 322
A. 280
B. 287
C. 294
D. 308
E. 322
26 Mar 2025, 01:13
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Short Version
One week difference for every single day is 7, so for 7 days
\( 329 - 7*7 = 280 \)
Option A - 280
Long Version
Number of shovels sold on the first day of March be \(x\).
Since sales decline by 1 shovel per day, the number of shovels sold each day of the first week follows an arithmetic sequence:
\( x, (x-1), (x-2), (x-3), (x-4), (x-5), (x-6) \)
The total sales for the first week are given as 329:
\( x + (x-1) + (x-2) + (x-3) + (x-4) + (x-5) + (x-6) = 329 \)
\( 7x - (0 + 1 + 2 + 3 + 4 + 5 + 6) = 329 \)
\( 7x - 21 = 329 \)
\( 7x = 350 \)
\( x = 50 \)
Thus, the number of shovels sold each day in the first week was:
\( 50, 49, 48, 47, 46, 45, 44 \)
For the second week, the trend continues, starting with 43 on the first day:
\( 43, 42, 41, 40, 39, 38, 37 \)
Total sales for the second week:
\( 43 + 42 + 41 + 40 + 39 + 38 + 37 = 280 \)
Option A - 280
One week difference for every single day is 7, so for 7 days
\( 329 - 7*7 = 280 \)
Option A - 280
Long Version
Number of shovels sold on the first day of March be \(x\).
Since sales decline by 1 shovel per day, the number of shovels sold each day of the first week follows an arithmetic sequence:
\( x, (x-1), (x-2), (x-3), (x-4), (x-5), (x-6) \)
The total sales for the first week are given as 329:
\( x + (x-1) + (x-2) + (x-3) + (x-4) + (x-5) + (x-6) = 329 \)
\( 7x - (0 + 1 + 2 + 3 + 4 + 5 + 6) = 329 \)
\( 7x - 21 = 329 \)
\( 7x = 350 \)
\( x = 50 \)
Thus, the number of shovels sold each day in the first week was:
\( 50, 49, 48, 47, 46, 45, 44 \)
For the second week, the trend continues, starting with 43 on the first day:
\( 43, 42, 41, 40, 39, 38, 37 \)
Total sales for the second week:
\( 43 + 42 + 41 + 40 + 39 + 38 + 37 = 280 \)
Option A - 280
26 Mar 2025, 10:23
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Bunuel
Let the number of shovels on day 1 be a.
The shovel decreases each day by one for the next 6 consecutive days of the week.
a + a-1+a-2 + a-3 + a-4 + a-5 + a-6 = 329
7a - 21 = 329
7a = 350
a = 50
The last day of first week is a-6 = 50 - 6 = 44.
In the next week, the initial value is a = 43. Since decreased by 1 compared to the previous day.
Next week we need to find 7a - 21.
= 7*(43) - 21
= 301 - 21
=280.
OPTION A
