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# Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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08 Jun 2016, 04:06
00:00

Difficulty:

45% (medium)

Question Stats:

83% (03:22) correct 17% (02:00) wrong based on 45 sessions

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Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?

A. 6.
B. 16.
C. 18.
D. 21.
E. 26.

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Posts: 7205
Re: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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08 Jun 2016, 04:37
Bunuel wrote:
Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?

A. 6.
B. 16.
C. 18.
D. 21.
E. 26.

let the price of notebook be N and that of pencil be P..
so P+N=5........so 15P+15N = 75.......(i)... so both P and N should be less than 5
also xP+ 15N = 93.....(ii)

subtract (i) from (ii).....
xP + 15N - 15P - 15N = 93-75 .............................(x-15)P=18 ......
Now both x and P are integers.... and P is less than 5, so value of P that are also factor of 18 are 1,2,3......
If P = 1, x-15 = 18/P = 18 or x=33....
If P = 2, x-15 = 18/2 = 9 or x = 24...
If P=3, x-15 = 18/3 = 6 or x=21...

So she could have purchased 21 or 24 or 33..
21 is in choices
D 21
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Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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08 Jun 2016, 06:00
I solved this question in a slightly different way:

5 = 1P + 1 N
93 = XP + 15N, where X is the number of pencils

Possible prices for 1P & 1N (integers):
N = 1 P = 4 then 15N = 15, 4X = 93 - 15 = 78, X = 19.5 (not an integer)
N = 2 P = 3 then 15N = 30, 3X = 93 - 30 = 63, X = 21 (the answer we were looking for, no need to continue calculations)
N = 3 P = 2
N = 4 P =1

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Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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08 Jun 2016, 11:00
1
Bunuel wrote:
Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?

A. 6.
B. 16.
C. 18.
D. 21.
E. 26.

Prices of each notebook and pencil range from 1 to 4 dollars and total amount of each one purchase must be 5 dollars

So here the formula =15*(price of each notebook)+(Number of pencil)*(price of each pencil) =93 ,here each of the variable must be integer

Putting the price of each notebook and each pencil We found that Only Answer Choice matches the equation because 15*2+3*21=93

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Re: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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09 Jun 2016, 02:47
Bunuel wrote:
Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?

A. 6.
B. 16.
C. 18.
D. 21.
E. 26.

N + P = 5 - (i)
GIven that both the prices are integers.

15N + xP = 93, x = ?
From (i), we know that
15N + 15P = 75

Therefore
(x - 15)P = 18 (ii) and both x and P are integers.
From (i), we also need to keep in mind that both N and P fall in the range (1, 4)

Checking the options for (ii)

A. 6. This will give a negative value. INCORRECT
B. 16. If x = 16, P = 18. INCORRECT
C. 18. If x = 18, P = 6 INCORRECT
D. 21. If x = 21, P = 6. CORRECT
E. 26. If x = 26, P is not an integer. INCORRECT

Correct Option: D
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Re: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were  [#permalink]

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26 Dec 2017, 11:40
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Re: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were &nbs [#permalink] 26 Dec 2017, 11:40
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# Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were

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