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The sum of the pre-tax costs of Item A and Item B is $300.

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Bunuel
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The sum of the pre-tax costs of Item A and Item B is $300. [#permalink] New post   04 Dec 2017, 05:07
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The sum of the pre-tax costs of Item A and Item B is $300. In Alumba, each item would be charged a fat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $3 more than it is in Alumba, then what is the pre-tax price of Item A?


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Re: The sum of the pre-tax costs of Item A and Item B is $300. [#permalink] New post   04 Dec 2017, 13:50
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Bunuel wrote:
The sum of the pre-tax costs of Item A and Item B is $300. In Alumba, each item would be charged a fat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $3 more than it is in Alumba, then what is the pre-tax price of Item A?


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Here for Alumba = 7% of (A+B) = 7% (300) =21

and for Aplandia it is $3 more i.e = 21 + 3 = 24

Now as per ques -

In Aplandia
0.05 A + 0.1 B = 24

or 0.05A + 0.1 (300 - A) =24 (Since , A+B = 300)

or 0.05A = 6

or A = 120, which is the pre tax value
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The sum of the pre-tax costs of Item A and Item B is $ 300. [#permalink] New post   23 Nov 2018, 05:38
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The sum of the pre-tax costs of Item A and Item B is $ 300. In Alumba, each item would be charged a flat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $ 3 more than it is in Alumba, then what is the pre-tax price of Item A?

Show: :: OA
120
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Re: The sum of the pre-tax costs of Item A and Item B is $ 300. [#permalink] New post   20 Dec 2018, 23:36
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Think about this, in Alumba, there is a flat tax on item A and B
so
A+B=300 without tax, but with tax in Alumba,
1.07(A+B)=1.07*300=$321

in Aplandia, Item A gets a 5% tax and item B gets a 10% tax

1.05A +1.10B=?

the tax in Aplandia adds to 3 dollars more than in Alumba

1.05A + 1.10B= $321+$3 =324

Make a system of equations.

1.05A+1.10B=324
A + B=300

get rid of B to find A

1.05A +1.10B =324
1.10(A+B) =1.10(300)

1.05A + 1.10B= 324
1.10A + 1.10B= 330

subtract top and bottom
.05A= 6
A=120
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Re: The sum of the pre-tax costs of Item A and Item B is $ 300. [#permalink] New post   21 Dec 2018, 09:52
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the key point here is to note that its the sum of the items A and B that is provided, not the price of them
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Re: The sum of the pre-tax costs of Item A and Item B is $ 300. [#permalink] New post   26 Jul 2019, 09:03
We can do the math just by the GAP of the tax amount-
Say, A's price =x, So, B=(300-x).
Now, .05(x)+.1(300-x) -21=3.
So, .05x+30-.1x=21+3.
-.05x=24-30=-6
so, x= -6/-.05
x=120 ( the price of A).
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Re: The sum of the pre-tax costs of Item A and Item B is $ 300. [#permalink] New post   11 Sep 2019, 07:46
Carcass wrote:
The sum of the pre-tax costs of Item A and Item B is $ 300. In Alumba, each item would be charged a flat 7%. In Aplandia, Item A is subject to 5% tax and Item B is subject to 10% tax. If the tax in Aplandia on the purchase of both items is exactly $ 3 more than it is in Alumba, then what is the pre-tax price of Item A?

Show: :: OA
120


Write out what we know mathematically:

PreTax: A + B = 300
Alumba: (A+B)1.07 = x
Aplandia: A(1.05) + B(1.10) = y

y - a = 3

What is A?
---------------
How to solve:
(300)*1.07 = 321 = x
so y = 3 + 321 = 324
plug into Aplandia and solve for B.
(324 - A*1.05)/1.10 = B
substitue into the PreTax
A + (324- A*1.05)/1.10 = 300
A(1.10) + 324 - A(1.05) = 330
A*0.05 = 6
A * (1/20) = 6
A = 120.
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Re: The sum of the pre-tax costs of Item A and Item B is $300. [#permalink] New post   15 Sep 2024, 22:01
Hello from the GRE Prep Club BumpBot!

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Re: The sum of the pre-tax costs of Item A and Item B is $300. [#permalink]
15 Sep 2024, 22:01
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