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

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Math Expert
Joined: 02 Sep 2009
Posts: 52935
Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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12 Mar 2015, 05:47
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Difficulty:

25% (medium)

Question Stats:

71% (01:20) correct 29% (01:40) wrong based on 132 sessions

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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.

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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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12 Mar 2015, 07:32
2A=75+B
A=75+B/2
we have that A+B=900

75+B/2+B=900

B=575

A=900-575=325
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Posts: 7334
Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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12 Mar 2015, 07:50
1
Bunuel wrote:
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.

given 2A=75+B....
Also A+B=900...
Substitute value of B..
A+2A-75=900..
A=325...
ans B..
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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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13 Mar 2015, 12:28
1
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
Math Expert
Joined: 02 Sep 2009
Posts: 52935
Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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15 Mar 2015, 21:12
Bunuel wrote:
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.

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.

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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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17 Mar 2015, 23:43

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

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

Setting up the equation for Alice

2x = (900-x) + 75

3x = 900 + 75

x = 325
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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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08 Jun 2017, 05:43
Bunuel wrote:
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.

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

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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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29 Sep 2018, 16:59
Bunuel wrote:
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

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

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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch  [#permalink]

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30 Sep 2018, 19:57
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...

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.

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Re: Alice and Bruce each bought a refrigerator, and the sum of their purch   [#permalink] 30 Sep 2018, 19:57
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