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16 Sep 2014, 00:56
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In October, Jack earned 25% more than in September; while in November, he earned 20% less than in October. If Jack earned $200 more in October than in September, what was his combined income for the autumn?
A. $1200
B. $1800
C. $2000
D. $2400
E. $2600
A. $1200
B. $1800
C. $2000
D. $2400
E. $2600
16 Sep 2014, 00:56
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Official Solution:
In October, Jack earned 25% more than in September; while in November, he earned 20% less than in October. If Jack earned $200 more in October than in September, what was his combined income for the autumn?
A. $1200
B. $1800
C. $2000
D. $2400
E. $2600
Let \(S\), \(O\), and \(N\) represent Jack's incomes in September, October, and November, respectively.
From the given, \(O = 1.25S\) and \(N = 0.8O\). Therefore, \(N = 0.8 *1.25S = S\). Given that \(O - S = 0.25S = \)200, we can deduce that \(S = \)800. Using this, \(O = 1.25*800 = \)1000 and \(N = S = \)800.
The total income for the autumn, \(S + O + N\), amounts to \(800 + 1000 + 800 = \)2600.
Answer: E
In October, Jack earned 25% more than in September; while in November, he earned 20% less than in October. If Jack earned $200 more in October than in September, what was his combined income for the autumn?
A. $1200
B. $1800
C. $2000
D. $2400
E. $2600
Let \(S\), \(O\), and \(N\) represent Jack's incomes in September, October, and November, respectively.
From the given, \(O = 1.25S\) and \(N = 0.8O\). Therefore, \(N = 0.8 *1.25S = S\). Given that \(O - S = 0.25S = \)200, we can deduce that \(S = \)800. Using this, \(O = 1.25*800 = \)1000 and \(N = S = \)800.
The total income for the autumn, \(S + O + N\), amounts to \(800 + 1000 + 800 = \)2600.
Answer: E
03 Feb 2017, 07:31
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Thanks for the explanation Bunuel. I came up with the same thing but just to lay it out in the format that I did...
S=S (Obviously)
O=1.25S
N=0.8O = 0.8(1.25S)
1.25S-0.8(1.25S)=200
1.25S-1S=200
0.25S=200
S=800
September = 800
October = 1.25(800) = 1,000
November = 0.8(1.25*800) = 0.8 (1,000) = 800
1,000+800+800 = 2,600
S=S (Obviously)
O=1.25S
N=0.8O = 0.8(1.25S)
1.25S-0.8(1.25S)=200
1.25S-1S=200
0.25S=200
S=800
September = 800
October = 1.25(800) = 1,000
November = 0.8(1.25*800) = 0.8 (1,000) = 800
1,000+800+800 = 2,600
