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A magazine stand owner sells cups of coffee, newspapers, and packs ofg

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A magazine stand owner sells cups of coffee, newspapers, and packs ofg  [#permalink]

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New post 13 May 2017, 10:28
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Difficulty:

  65% (hard)

Question Stats:

62% (02:45) correct 38% (03:50) wrong based on 67 sessions

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A magazine stand owner sells cups of coffee, newspapers, and packs ofgum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only

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A magazine stand owner sells cups of coffee, newspapers, and packs ofg  [#permalink]

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New post 13 May 2017, 12:04
(Number sold) Coffee = 2Gum = 3NewsPaper
(Cost) --------- $1.25 --- $.35 ------$.50

If the number of coffees sold of coffee is x,
Total gross sale can be given by 1.25x + 2x(0.35) + 3x(0.50) = 3.45x

If x=100, I will be possible as a gross sale
If x=17, II will be possible as a gross sale
However at x=6, 20.7 will be the gross sale
and x=7, 24.15 will be the gross sale. Hence, we cannot have III as a possibility for gross sale.

So Option B is the correct choice.
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A magazine stand owner sells cups of coffee, newspapers, and packs ofg  [#permalink]

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New post 13 May 2017, 12:32
1
It is stated that the ration of Coffee:Newspaper:Gum sold is 1x:2x:3x ----> (1)

The amount of the coffee mentioned is $1.25 , Gum is $0.35 and Newspaper is $0.50 ----->(2)

Let x be the no: of cups of coffee sold be x.

From eq (1) & eq (2)
Total amount of the gross sales is 1.25*x+0.70*x+1.5*x = 3.45*x

Looking at the options :

For option A . If we put the value of x =100 we get 345 ----> It could be the total amount of the gross sales.

For option B we can do the following ----> 58.65 = 3.45*x----> x = 58.65/3.45 = 17 ------>It could be the total amount of the gross sales.

For option C we can do the following ----> 22.15 = 3.45*x -----> x = 443/69 = 6.42.... ------> It cannot be the total amount of the gross sales.

Option B is the correct
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Re: A magazine stand owner sells cups of coffee, newspapers, and packs ofg  [#permalink]

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New post 22 May 2017, 23:21
1
Let Number of coffee cups sold = n
Then number of gum packs sold = 2n
and number of newspapers sold = 3n

We are given the prices. So gross sales =
n*1.25 + 2n*0.35 + 3n*0.5 = 3.45n

So the sales will be $ 3.45n where n Must be a positive integer

I. Put 3.45n = 345, n =100 which is an integer. Possible
II. Put 3.45n = 58.65, n =17 which is an integer. Possible
III. Put 3.45n = 22.15, n is not an integer. Impossible

Only I and II are possible. Hence answer is B
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A magazine stand owner sells cups of coffee, newspapers, and packs ofg  [#permalink]

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New post 20 Jan 2018, 06:44
1
SajjadAhmad wrote:
A magazine stand owner sells cups of coffee, newspapers, and packs ofgum. Compared to the number of cups of coffee he sells, he sells twice as many packs of gum, and three times as many newspapers. If he charges $1.25 for a cup of coffee, $.50 for a newspaper, and $.35 for a pack of gum, and sells no other items, which of the following could be the amount of his total gross sales on a given day?

I.$345.00
II.$58.65
III.$22.15

A. I only
B. I + II only
C. I + III only
D. II and III only
E. I, II and III only


We can let the number of packs of gum = g, the number of newspapers = n, and the number of cups of coffee = c, and create the equations:

2c = g

and

3c = n

We need to determine the value of:

1.25c + 0.5n + 0.35g

Substituting, we have:

1.25c + 0.5(3c) + 0.35(2c)

1.25c + 1.5c + 0.7c

3.45c = ?

Now let’s check which Roman numerals is an integer multiple of 3.45.

I.$345.00
Since 345/3.45 = 100, we see that I could be the total gross sales.

II.$58.65
Since 58.65/3.45 = 17, we see that II could be the total gross sales.

III.$22.15
Since 22.15/3.45 = 6.42, we see that III could NOT be the total gross sales.

Answer: B
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A magazine stand owner sells cups of coffee, newspapers, and packs ofg &nbs [#permalink] 20 Jan 2018, 06:44
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