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Difficulty:
35%
(medium)
Question Stats:
80% (03:11) correct
20%
(03:27)
wrong
based on 50
sessions
History
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Sumitra has to solve 384 questions. She decides to solve a particular number of questions per day to complete the task in a certain number of days. Shalini, her friend, suggests that if she solves eight more questions per day than what Sumitra has decided, she will take eight fewer days to finish the task than what Sumitra has calculated. In how many days can the task be completed if Sumitra follows what Shalini suggested?
A. 10
B. 12
C. 14
D. 16
E. 18
_________________
A. 10
B. 12
C. 14
D. 16
E. 18
_________________
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We can set up an equation by translating the word problem above.
Sumitra has to solve 384 questions.
Number of Questions / Questions per day = Days
If Sumitra does not follow her friends suggestions, she will take 384/x days. If she follows her friend’s suggestion of reading 8 more pages per day (x+8) she will take 384/x+8 days. The difference in number of days between both rates is 8.
We can set up an equation as such:
384/x - 384/x+8 = 8
Next,
384(x+8) - 384x = 8(x)(x+8) —> multiple the whole equation by LCM (x)(x+8) to simplify the fractional denominators.
384x + 384(8) - 384x = 8x^2 + 64x
0 = 8x^2 + 64x - 384(8)
0 = x^2 + 8x- 384
0 = (x + 24)(x - 16)
x = -24 or x = 16
Since pages per day cannot be negative, x = 16
Number of days without suggestion:
384/16 = 24 days
Number of days with suggestion:
384/24 = 16 days
24 days - 16 days = 8 fewer days following suggestion
IMO Option D
Posted from my mobile device
Sumitra has to solve 384 questions.
Number of Questions / Questions per day = Days
If Sumitra does not follow her friends suggestions, she will take 384/x days. If she follows her friend’s suggestion of reading 8 more pages per day (x+8) she will take 384/x+8 days. The difference in number of days between both rates is 8.
We can set up an equation as such:
384/x - 384/x+8 = 8
Next,
384(x+8) - 384x = 8(x)(x+8) —> multiple the whole equation by LCM (x)(x+8) to simplify the fractional denominators.
384x + 384(8) - 384x = 8x^2 + 64x
0 = 8x^2 + 64x - 384(8)
0 = x^2 + 8x- 384
0 = (x + 24)(x - 16)
x = -24 or x = 16
Since pages per day cannot be negative, x = 16
Number of days without suggestion:
384/16 = 24 days
Number of days with suggestion:
384/24 = 16 days
24 days - 16 days = 8 fewer days following suggestion
IMO Option D
Posted from my mobile device
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