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Gen Arithematics

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by manu.pant » Tue May 11, 2010 7:24 am
At the wholesale store you can buy an 8 pack of Hot dog for $1.55, an 20 pack for $3.05 , and 250 pack for $22.95. What is the greatest nos of HDs that u can buy from the store for $200.

Ans: 2100
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by iamseer » Tue May 11, 2010 8:36 am
maximizing the pack with 250 will allow maximizing over all number that can be bought with 200.
22.95*8 is 16.40 less than 200 ---- 250*8= 2000

now to maximize the number that can be bought with 16.40 we need to buy packs of 20
3.05*5 is 1.15 less than 16.40 ---- 20*5=100

with the remaining 1.15 nothing can be bought.

Since 1.15 remains, we check if buying packs of 8 would have bought us more than 200. For that we have to buy more than 25 packets.
1.55*26 >> 16.40
as we have 16.40 only, we can't buy more than 200 with this option either.

So, maximum that can be bought is 2100

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Re: Gen Arithematics

by Scott@TargetTestPrep » Tue Nov 17, 2020 2:00 pm
manu.pant wrote: ↑
Tue May 11, 2010 7:24 am
 At the wholesale store you can buy an 8 pack of Hot dog for $1.55, an 20 pack for $3.05 , and 250 pack for $22.95. What is the greatest nos of HDs that u can buy from the store for $200.

Ans: 2100
Solution:

The unit price (i.e., price per hot dog) of an 8-pack is $1.55/8 ≈ $0.19, that of a 20-pack is $3.05/15 ≈ $0.15 and that of a 250-pack is $22.95/250 ≈ $0.09. Since the 250-pack has the lowest unit price, we should buy as many 250-packs as we can.

With $200, we can buy 200/22.95 = 8 complete 250-packs, and we will have 200 - 8 x 22.95 = $16.40 remaining.

Next, we will buy as many 20-packs, which will be 16.40/3.05 = 5 complete 20-packs, and we will have 16.40 - 5 x 3.05 = $1.15 remaining.

We note that $1.15 is insufficient for additional purchases. Thus, we have purchased 8 x 250 + 5 x 20 = 2,100 hot dogs.

Answer: 2,100

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