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A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i

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A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 10 May 2018, 16:53
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A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts in an order and $10 per T-shirt for each additional T-shirt in the order. If the charge for an order of T-shirts was $1500, how many T-shirts were in the order?

A) 90
B) 125
C) 140
D) 150
E) 200
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Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 10 May 2018, 21:05
Let extra number of t shirt after 50 be x

12*50 + 10x=1500
10x=900
X=90

Total t-shirt=90+50=140

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Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 10 May 2018, 22:51
Total charge for the order = $1500
Charge @ $12 per T shirt for the first 50 = 50 * 12 = 600

Charge @ $10 per T shirt beyond the first 50 = 1500 - 600 = 900.
Number of T Shirts in the order beyond the first 50 = 900/10 = 90.

Total number of T shirts in the order = 50 + 90 = 140
Choice C
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A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 11 May 2018, 17:05
alanforde800Maximus wrote:
A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts in an order and $10 per T-shirt for each additional T-shirt in the order. If the charge for an order of T-shirts was $1500, how many T-shirts were in the order?

A) 90
B) 125
C) 140
D) 150
E) 200

The trap here is forgetting to account for or to "add back" the first 50

I. Arithmetic
How many T-shirts were there in an order charge of $1500?

Cost 1: $12 per T-shirt for first 50 = $600

Cost 2: $10 per T-shirt, for any number \(x\) T-shirts, AFTER the first 50

T-shirt order total: $1500

(1) 50 T-shirts cost $600
($1500 - $600) = $900 remain

(2) $900 = how many T-shirts?
$900/$10 per shirt = 90 shirts

Number of T-shirts in the order?
50 + 90 = 140

Answer C

II. Algebra
Let \(x\) = # of T-shirts

\((12)(50) + (10)(x-50) = 1500\)
\(600 + 10x - 500 = 1500\)
\(10x + 100 = 1500\)
\(10x = 1400\)
\(x = 140\)


Answer C
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Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 14 May 2018, 16:53
alanforde800Maximus wrote:
A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts in an order and $10 per T-shirt for each additional T-shirt in the order. If the charge for an order of T-shirts was $1500, how many T-shirts were in the order?

A) 90
B) 125
C) 140
D) 150
E) 200


We can let n = the total number of shirts and create the equation:

1500 = 12(50) + 10(n - 50)

1500 = 600 + 10n - 500

1400 = 10n

140 = n

Answer: C
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Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 22 May 2018, 05:45
alanforde800Maximus wrote:
A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts in an order and $10 per T-shirt for each additional T-shirt in the order. If the charge for an order of T-shirts was $1500, how many T-shirts were in the order?

A) 90
B) 125
C) 140
D) 150
E) 200


Simply make an equation:

12*50 +10*x = 1500 (Total order value)

600 + 10*x = 1500

x = (1500 - 600)/9

x = 90

So, total T shirts = 90 + 50 = 140

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Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i [#permalink]

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New post 22 May 2018, 06:08
Another approach to this problem is by back solving. As always, take a look at the answer choices after reading the prompt and think about what approach makes sense to you e.g. if have strong algebra fundamentals take that route, etc.

I typically start with B then move to D depending on how big or small the choice is compared to what I'm looking for.

Using B, we know the first 50-shirts are $12 a pop (50 shirts at $10 is $500, 50 shirts at $2 is $100; therefore, 50 shirts at $12 is $600). The remaining 75 shirts at $10 is $750. $600 + $750 = $1350 which is too low compared to the $1500 we need. Therefore eliminate B and A (choice A is smaller in value then choice B).

Move to choice D. Same approach as testing choice B and since 100 shirts remain we know that portion costs $1000. Total is $1000 + $600 = $1600, which is way larger in value than the $1500 we're looking for. Therefore, eliminate D and E and select Answer Choice C.
Re: A T-shirt supplier charges $12 per T-shirt for the first 50 T-shirts i   [#permalink] 22 May 2018, 06:08
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