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A store currently charges the same price for each shirt it sells. If

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Math Expert
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A store currently charges the same price for each shirt it sells. If  [#permalink]

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New post 02 Jan 2018, 00:27
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (02:31) correct 23% (02:17) wrong based on 39 sessions

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A store currently charges the same price for each shirt it sells. If  [#permalink]

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New post 02 Jan 2018, 06:32
2
Bunuel wrote:
A store currently charges the same price for each shirt it sells. If the current price of each shirt were to be decreased by $2, 10 more shirts could be bought for $315. What is the current price of each shirt?

A. $6
B. $7
C. $9
D. $10
E. $12

The figure $315 and the answer choices are a big cue: use divisibility rules.

There cannot be partial shirts. $315 must be divisible by the cost per shirt.

That rules out A, D, and E.

A) $6. $315 must be divisible by 2 and 3. It not divisible by 2, hence not divisible by 6. REJECT

D) $10: $315/$10 = 31.5 shirts. OR: $315 does not end in 0. (Not an even number divisible by 5, not divisible by 2 and 5.) REJECT

E) $12: $315 must be divisible by 6 and 2. From above, $315 is not divisible by 6. REJECT

That leaves B and C.

Try C) $9
$315/$9 = 35 shirts
Price decreases by $2
($9 - $2) = $7
$315/$7 = 45 shirts = 10 more shirts if price is $7

Answer C
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Re: A store currently charges the same price for each shirt it sells. If  [#permalink]

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New post 03 Jun 2020, 19:21
Bunuel, generis ,

I landed up in below mentioned equation, kindly suggest

Let , no. of shirt purchased = x,
initial price of shirt = p
dec by $2
( x+10)(p-2) = 315
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Re: A store currently charges the same price for each shirt it sells. If  [#permalink]

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New post 03 Jun 2020, 19:44
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Re: A store currently charges the same price for each shirt it sells. If  [#permalink]

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New post 03 Jun 2020, 20:42
C.


Price of each shirt = x
Total number of shirts =y

xy = 315. ----eq 1
(x-2)(y+10=315
xy +10x -2y -20 =315
putting value of xy = 315
315 +10x -2y -20 = 315
or 5x - y -10 =0
putting y = 315/x

5x - 315/x -10= 0
5x^2 - 10x - 315= 0
or x^2 - 2x - 63 = 0

Solving: x = 9
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Re: A store currently charges the same price for each shirt it sells. If   [#permalink] 03 Jun 2020, 20:42

A store currently charges the same price for each shirt it sells. If

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