Alice and Bruce each bought a refrigerator, and the sum of their purch

Question

Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275 
B. $325 
C. $425 
D. $575 
E. $625

Kudos for a correct  solution .

23a2012 · Answer

the answer is B
2A=75+B
A=75+B/2
we have that A+B=900

75+B/2+B=900

B=575

A=900-575=325

chetan2u · Answer

given 2A=75+B....
Also A+B=900...
Substitute value of B..
A+2A-75=900..
A=325...
ans B..

smartyguy · Answer

Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275 
B. $325 
C. $425 
D. $575 
E. $625

Given

2A-75 = B--1
A+B =900--2

Substituting value of B from 2 in 1

--> A = 325
hence B

Regards
SG

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

This is a relatively easy word problem. Let A be Alice’s share, and B, Bruce’s share. Clearly A + B = 900. We also are told that 2A = B + 75. To solve, use  substitution . Solve this for B:
B = 2A – 75.

Now, plug this into the first equation:
A + (2A – 75) = 900
3A = 900 + 75
A = 300 + 25 = $325

Alice’s share is $325.

Answer = (B).

PareshGmat · Answer

Answer = B = 325

Alice ................ Bruce ................... Total

x ....................... 900-x ...................... 900

Setting up the equation for Alice

2x = (900-x) + 75

3x = 900 + 75

x = 325

Mo2men · Answer

Let Alice's payment = A

Let Bruce's payment = B

A + B =900..............1

2A = B + 75.............2

From equation 1: B = 900 - A

Substitute in 2

2A = 900 - A + 75

3A = 975.................No Need to perform any calculations. If it is 900 then A = 300, so we need number little bit higher 300

Answer: B

ScottTargetTestPrep · Answer

We can let a = the amount Alice paid for her refrigerator and b = the amount Bruce paid for his refrigerator. Therefore,

a + b = 900

and

2a = b + 75

Isolating b in the second equation, we have b = 2a - 75. Substituting this for b in the first equation, we have:

a + 2a - 75 = 900

3a = 975

a = 325

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

We're told that Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. We're also told that TWICE of what Alice paid was $75 MORE than what Bruce paid. We're asked what did Alice paid for her refrigerator. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, as an estimate, if Bruce paid exactly twice what Alice paid, then their two purchase prices would have been 600 and 300, respectively. However, we know that that did NOT happen (since "twice what Alice paid was $75 MORE than what Bruce paid"). Thus, Alice would have paid a bit more than $300. Let's TEST Answer B first...

Answer B: $325 
IF.... Alice paid $325, then 
Bruce paid 2($325) - $75 = $650 - $75 = $575 
Total paid by both = $325 + $575 = $900 
This is an exact match for what we were told, so this MUST be the answer.

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

This question lends itself nicely to  testing the answer choices

We'll start with answer choice C ( $425 ), the middle value. 
If Alice paid  $425 , how much did Bruce pay? 
Given: twice of what Alice paid was $75 more than what Bruce paid
Two times $425 = $850, so Bruce paid  $775  (since $850 - $75 =  $775 
COMBINED PAYMENTS =  $425  +  $775  = $1200
No good - we need the combined payments to be $900
ELIMINATE C
We can also ELIMINATE D and E, because those values will yield an even greater values of the combined payments.

Now let's try B ( $325 )
Given: twice of what Alice paid was $75 more than what Bruce paid
Two times $325= $650, so Bruce paid  $575  (since $650 - $75 =  $575 
COMBINED PAYMENTS =  $325  +  $575  = $900
Perfect!!!

Answer: B

Cheers,
Brent

BrentGMATPrepNow · Answer

We can also solve the question algebraically, using 1 variable or 2 variables. 
Here's a solution with 1 variable:

Given:   Twice of what Alice paid was $75 more than what Bruce paid   
Let x = the amount Alice paid
So, 2x - 75 = the amount Bruce paid

Given:   The sum of their purchases was $900   
So, (the amount Alice paid) + (the amount Bruce paid) = 900
We get: x + (2x - 75) = 900
Simplify: 3x - 75 = 900
Solve: x = 325

Answer: B

Cheers,
Brent

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