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# A sporting goods store has a section that displays baseball caps, and

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Joined: 28 May 2014
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A sporting goods store has a section that displays baseball caps, and [#permalink]

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17 Nov 2017, 09:21
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A sporting goods store has a section that displays baseball caps, and each shelf in the section displays 10 caps. After 16 caps were sold, each shelf was left with 7 caps except for the final shelf, which held 9 caps. How many shelves are in the section displaying baseball caps?

(a) 3
(b) 5
(c) 6
(d) 7
(e) 11

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Re: A sporting goods store has a section that displays baseball caps, and [#permalink]

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17 Nov 2017, 09:59
10n - (7(n-1) +9) = 16
N= 6
SC Moderator
Joined: 22 May 2016
Posts: 1681
A sporting goods store has a section that displays baseball caps, and [#permalink]

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17 Nov 2017, 10:11
saswata4s wrote:
A sporting goods store has a section that displays baseball caps, and each shelf in the section displays 10 caps. After 16 caps were sold, each shelf was left with 7 caps except for the final shelf, which held 9 caps. How many shelves are in the section displaying baseball caps?

(a) 3
(b) 5
(c) 6
(d) 7
(e) 11

Before caps were sold there were 10 caps per shelf. (6*10) = 60 caps
16 are sold. (60-16) = 44 remain

After the caps are sold, there are 7 caps on all but the last shelf, which has 9.

So remaining caps are:
1) 7 caps on 5 shelves; and
2) 9 caps on 1 shelf

1) 5 * 7 = 35
2) 35 + (9)(1) = 44

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Re: A sporting goods store has a section that displays baseball caps, and [#permalink]

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17 Nov 2017, 10:14
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Expert's post
saswata4s wrote:
A sporting goods store has a section that displays baseball caps, and each shelf in the section displays 10 caps. After 16 caps were sold, each shelf was left with 7 caps except for the final shelf, which held 9 caps. How many shelves are in the section displaying baseball caps?

(a) 3
(b) 5
(c) 6
(d) 7
(e) 11

algebra...
Let the number be x, so total = 10x
after taking out 16, x-1 have 7 each and 1 has 9..
so $$10x-16=7(x-1)+9........10x-16=7x-7+9.....3x=16+9-7=18...x=6$$

another way..
if you remove 16, it leads to 3 less in x-1 and 1 less in last one..
so $$16= 3(x-1)+1.....16=3x-3+1.....3x=18...x=6$$

C
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Re: A sporting goods store has a section that displays baseball caps, and [#permalink]

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27 Nov 2017, 12:14
saswata4s wrote:
A sporting goods store has a section that displays baseball caps, and each shelf in the section displays 10 caps. After 16 caps were sold, each shelf was left with 7 caps except for the final shelf, which held 9 caps. How many shelves are in the section displaying baseball caps?

(a) 3
(b) 5
(c) 6
(d) 7
(e) 11

Since 16 caps were sold, we can say that 3 were removed from 5 shelves and 1 was removed from the 6th shelf. So there are 6 total shelves.

Alternate Solution:

We can let n = the number of shelves. Thus the original number of caps is 10n. After 16 caps were sold, n - 1 shelves have 7 caps each and the last shelf has 9 caps; so we can create the following equation:

10n - 16 = 7(n - 1) + 9

10n - 16 = 7n - 7 + 9

3n = 18

n = 6

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Re: A sporting goods store has a section that displays baseball caps, and   [#permalink] 27 Nov 2017, 12:14
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