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Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50,

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Bunuel
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Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, [#permalink] New post   05 May 2017, 03:24
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Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, or $0.25 each. What is the greatest number of pens that can be purchased for $57.75?

A. 475
B. 457
C. 439
D. 423
E. 357
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Re: Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, [#permalink] New post   05 May 2017, 05:07
Cost per pen, when we buy a pack of 100 pens = $ 12/100 = $0.12
Cost per pen, when we buy a pack of 50 pens = $ 8/50 = $0.16
Cost per pen, when we buy a single pen = $0.25

So, to maximise the number of pens in a fixed amount, objective is to have as many 'packs of 100' as possible, followed by as many 'packs of 50' as possible, followed by single pens.

No of 'packs of 100' = 57.75/12 = 4 (quotient is 4). 12*4 = 48, this leaves us with 57.75 - 48 = $9.75 (and now we have 400 pens)

No of 'packs of 50' = 9.75/8 = 1 (quotient is 1). This leaves us with $1.75 (and we have an additional 50 pens)

In remaining amount, we can get 1.75/0.25 = 7 single pens.

Thus max no of pens possible = 400+50+7 = 457. hence B
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Re: Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, [#permalink] New post   05 May 2017, 12:38
If he purchases 4(12$ packs),1(8$ pack) and 7(.25$ packs) he will exhaust 57.75$.

Since one 12$ pack gives him 100 pens, one 8$ pack gives him 50 and each additional pen costs him .25$, he will get 4*100 + 1*50 + 7*1 =457 pens(Option B)

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Re: Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, [#permalink] New post   12 May 2017, 13:20
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Bunuel wrote:
Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, or $0.25 each. What is the greatest number of pens that can be purchased for $57.75?

A. 475
B. 457
C. 439
D. 423
E. 357


With $57.75, we can buy (at most) four 100-packs.

After we purchase four 100-packs, we have 57.75 - 48 = $9.75 left over.

With $9.75, we can buy (at most) one 50-pack.

After we purchase one 50-pack, we have 9.75 - 8 = $1.75 left over.

Finally, we can purchase 1.75/0.25 = 7 individual pens.

Thus, the maximum number of pens we can purchase is 400 + 50 + 7 = 457 pens.

Answer: B
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Re: Bino pens can be purchased for $12 per pack of 100, $8 per pack of 50, [#permalink]
12 May 2017, 13:20
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