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16 Nov 2020, 03:30
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Difficulty:
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Question Stats:
71% (02:53) correct
29%
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wrong
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Jennifer has $400 more than Brian has. If she were to give Brian 20% of her money, then Brian would have 2/3 of the amount of money that Jennifer would then have. How much money does Brian currently have (before exchanging money)?
A. 100
B. 120
C. 160
D. 180
E. 200
A. 100
B. 120
C. 160
D. 180
E. 200
16 Nov 2020, 04:21
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Bunuel
There are 2 ways of going about. First is the method of equations and the second is by using the options.
Let the amount of money with Brian = x
Therefore the amount with Jennifer = x + 400
If Jennifer gives 20% away, then amount given to Brian = 0.2 * (x + 400) = 0.2x + 80
Amount with Brian now = x + 0.2x + 80 = 1.2x + 80
The remaining amount with Jennifer = 80% of (x + 400) = 0.8x + 320
Given that Brian has 2/3 rd of what Jennifer has, i.e 1.2x + 80 = \(\frac{2}{3}\) * (0.8x + 320)
Solving for x, we get 3(1.2x + 80) = 2(0.8x + 320)
3.6x + 240 = 1.6x + 640
2x = 400
x = 200
The second method is using the options. Since the options give us the amount Brian has initially, we can calculate and see which option matches the requirements.
We need to calculate Jennifer's final amount and see if it is divisible by 3, as Brian will have 2/3rd of that amount
Option A: B = 100, J = 100 + 400 = 500
Brians final amount = 100 + 20% of 500 = 200
Jennifers final amount = 80% of 500 = 400. Now this is not divisible by 3, so this option gets eliminated.
Option B: B = 120, J = 120 + 400 = 520
Brians final amount = 100 + 20% of 520 = 204
Jennifers final amount = 80% of 520 = 416. This is not divisible by 3, so this option gets eliminated.
Option C: B = 160, J = 160 + 400 = 560
Brians final amount = 100 + 20% of 560 = 212
Jennifers final amount = 80% of 560 = 448. This is not divisible by 3, so this option gets eliminated.
Option D: B = 180, J = 180 + 400 = 580
Brians final amount = 100 + 20% of 580 = 216
Jennifers final amount = 80% of 580 = 464. This is not divisible by 3, so this option gets eliminated.
Option E
Arun Kumar
17 Nov 2020, 00:16
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"Jennifer has $400 more than Brian has"
J = B + 400
"If Jennifer gives Brian 20% of her money, then Brian has 2/3 of the money that Jennifer would then have."
Jennifer would give Brian ------> 20%(J)
Jennifer would then have left to herself ------> 80%(J)
B + 20%(J) = 2/3 * [80% * (J)]
B + (1/5)J = 2/3 * [ (4/5) * J]
B + J/5 = (8/15) * J
----multiply both sides by *15----
15B + 3J = 8J
15B = 5J
3B = J --------> Plug this back into the Original Equation for "J" to find the amount of money Brian has now
J = B + 400
3B = B + 400
2B = 200
B = $200
-E-
J = B + 400
"If Jennifer gives Brian 20% of her money, then Brian has 2/3 of the money that Jennifer would then have."
Jennifer would give Brian ------> 20%(J)
Jennifer would then have left to herself ------> 80%(J)
B + 20%(J) = 2/3 * [80% * (J)]
B + (1/5)J = 2/3 * [ (4/5) * J]
B + J/5 = (8/15) * J
----multiply both sides by *15----
15B + 3J = 8J
15B = 5J
3B = J --------> Plug this back into the Original Equation for "J" to find the amount of money Brian has now
J = B + 400
3B = B + 400
2B = 200
B = $200
-E-
