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# Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does

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Math Expert
Joined: 02 Sep 2009
Posts: 61302
Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does  [#permalink]

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08 Nov 2018, 02:07
00:00

Difficulty:

55% (hard)

Question Stats:

67% (03:12) correct 33% (02:47) wrong based on 42 sessions

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Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does, and x is the sum, in cents, of the money in their piggy banks. If half of the money in Emma’s piggy bank is moved to Robert’s and then x cents is added to each piggy bank, how much money, in cents, will Robert’s piggy bank then contain?

A. 3x/4 - 3

B. 3x/4 + 3

C. 7x/4 - 3

D. 7x/4 + 3

E. 3x/2 + 6

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Re: Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does  [#permalink]

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08 Nov 2018, 03:26
Approach 1: Number plug in:

Say R=2, so E=14, and x=R+S= 16
Now We need to find :
E/2 +R +X = 7+2+16=25
Plug in value of x in each option:
Option A gives: 9 NO
Option B gives: 15 NO
Option C gives: 25 Bingo….

Approach 2 Algebra:

Given
E=R+12 and E+R =X
So 2R+12 =X
R= (X-12)/2
E= R +12 = (X-12)/2 +12 = (X+12)/2
From Question:
R+X+ E/2 =?
(X-12)/2 + X + (X+12)/4
(2X-24+4X+ X+12)/4
(7X-12)/4
7X/4 - 3
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Re: Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does  [#permalink]

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24 Jan 2020, 06:28
Bunuel wrote:
Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does, and x is the sum, in cents, of the money in their piggy banks. If half of the money in Emma’s piggy bank is moved to Robert’s and then x cents is added to each piggy bank, how much money, in cents, will Robert’s piggy bank then contain?

A. 3x/4 - 3
B. 3x/4 + 3
C. 7x/4 - 3
D. 7x/4 + 3
E. 3x/2 + 6

e=r+12
x=e+r=2r+12
2r+12=x, 2r=x-12, r=x/2-6

robert after emma/2 and x:
r+e/2+x, r+(r+12)/2+x, (2r+r+12)/2+x
(x+x/2-6)/2+x, (3x/2-6)/2+x,
3x/4-3+x, 7x/4-3

Ans (C)
Re: Emma’s piggy bank contains 12 cents more than Robert’s piggy bank does   [#permalink] 24 Jan 2020, 06:28
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