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The average American spends y dollars on food per month, except during

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The average American spends y dollars on food per month, except during  [#permalink]

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New post 29 Jul 2017, 00:19
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The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A)9y – xy/100

B)9y + xy

C)9y – xy

D)(9y-xy)/9

E)y-xy/6
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Re: The average American spends y dollars on food per month, except during  [#permalink]

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New post 29 Jul 2017, 00:48
1
Spends in Jan = (y - xy/100)
In other 8 months 8y

Total 8y + (y - xy/100)
=9y - xy/100 --A
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The average American spends y dollars on food per month, except during  [#permalink]

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New post 29 Jul 2017, 10:06
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srikanth9502 wrote:
The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following reepresents food purchases, in dollars, for the first 9 months of a year?

A)9y – xy/100

B)9y + xy

C)9y – xy

D)(9y-xy)/9

E)y-xy/6

Assign values.

Let y dollars per month be 10
Let x percent less for January be 10

Eight month total is (8 * 10) = $80
January total is (.90)(10) = $9
Total for nine months = $89

With y = 10 and x = 10, find the answer choice that yields $89.

Answers B, C, D, and E can be eliminated quickly.

Answer B is 9y + xy. 9y = (9*10) = 90 is too high already. Adding anything will make it higher.

Answer C, 9y – xy. Easy and quick calculation shows result is negative.
(9*10) + (10*10) =
(90) - (100) = -10

If C is negative, then Answer D, (9y-xy)/9, is too. Its numerator is identical to answer C.

If C is negative with (9y - xy), then Answer E's numerator, 1y - xy, will be more negative.

Answer A, which initially looked strange because I read the denominator incorrectly, remains: 9y – xy/100

(9 * 10) - \(\frac{(10*10)}{100}\) =

90 - 1 = 89
Answer A
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Re: The average American spends y dollars on food per month, except during  [#permalink]

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New post 12 Aug 2017, 11:48
The amount for nine months: 9y

The amount for the January: y(x/100) = xy/100

What we're looking for is the amount spent for the first eight months of the year which would be the difference between nine months and the amount spent in January. This can be written algebraically as: 9y - xy/100

Which is answer choice A.
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The average American spends y dollars on food per month, except during  [#permalink]

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New post 13 Jan 2019, 08:01
Just fell over this question and I'm wondering why C isn't the right answer. (9*10 - 0.1*10 = 89)

My approach was the exact same as generis', with the exception that I Plugged in 0.1 for x, because in the statement it says x=percent.

Why do I have to plug in 10 now? I don't get it.
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Re: The average American spends y dollars on food per month, except during  [#permalink]

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New post 20 Jan 2019, 05:45
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srikanth9502 wrote:
The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A)9y – xy/100

B)9y + xy

C)9y – xy

D)(9y-xy)/9

E)y-xy/6


This is a Variables in the Answer Choices question (VIAC). This question type can be answered algebraically or using the INPUT-OUTPUT approach.
Let's solve the question algebraically.

The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months.
In other words, January's food purchase amount is x percent less than y
x percent = x/100
So, x percent of y = (x/100)(y) = xy/100
So, January's food purchase amount = y - xy/100

Which of the following represents food purchases, in dollars, for the first 9 months of a year?
January's food purchase amount = y - xy/100
The food purchase amount for EACH of the other 8 months = y

So, the TOTAL cost = y - xy/100 + y + y + y + y + y + y + y + y
= y - xy/100 + 8y
= 9y - xy/100

Answer: A

Cheers,
Brent

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Re: The average American spends y dollars on food per month, except during  [#permalink]

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New post 20 Jan 2019, 06:34
srikanth9502 wrote:
The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A)9y – xy/100

B)9y + xy

C)9y – xy

D)(9y-xy)/9

E)y-xy/6


Plug in some values and check...

Let y = 100 & y = 10

So, Feb to September , monthly expenses is 100*8 = 800

Expenses in January is 90

So, The total expense for the first 9 month is 800 + 90 = 890

NOw, Check the options -

(A) 9y – xy/100 = 9*100 -10*100/100 => 890 ; Thus, Answer must be (A)
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Re: The average American spends y dollars on food per month, except during  [#permalink]

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New post 20 Jan 2019, 07:47
srikanth9502 wrote:
The average American spends y dollars on food per month, except during January, when food purchases are x percent lower than they are in other months. Which of the following represents food purchases, in dollars, for the first 9 months of a year?


A)9y – xy/100

B)9y + xy

C)9y – xy

D)(9y-xy)/9

E)y-xy/6


Let the average American spends 10 dollars on food per month

January, when food purchases are 10 percent lower than they are in other months

For the first 9 months of a year, following represents food purchases
80 + 10% 90 = 89

I was looking for a relationship in which a reduction was been made, B and C removed

D is / something by 9 ->Will reduce the value further Out

E is / something by 6 ->Will reduce the value further Out
A)9y – xy/100
90 - 10* 10/100
= 89
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Re: The average American spends y dollars on food per month, except during &nbs [#permalink] 20 Jan 2019, 07:47
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