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Arithmetic operations of rational numbers

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Arithmetic operations of rational numbers [#permalink] New post 30 Jan 2012, 16:24
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A certain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable. Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes.

OG-#125

The only problem I am having with is figuring out the last step.

I found difference and now must solve for 10.2/54. I tried doing long division (which will not work well in a 2 minute time-frame) and then tried breaking up the numerator and denominator. What do you recommend I do for similar questions like this where long division is not optimal and the numbers do not break up easily. I got it down to 17/90 but how am I supposed to know this represents .19?

Thanks
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Re: Arithmetic operations of rational numbers [#permalink] New post 30 Jan 2012, 20:15
With these type of problems it is best to round and estimate.
so you have 10.2/54 I would round it to 10/54 would make it easier to work out and you just choose the answer choice that is closest to your answer

so 10/54 would be .185 and just round it up to .19 which is the answer
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Re: Arithmetic operations of rational numbers [#permalink] New post 30 Jan 2012, 21:43
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jmehrabi wrote:
A certain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable. Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes.

OG-#125

The only problem I am having with is figuring out the last step.

I found difference and now must solve for 10.2/54. I tried doing long division (which will not work well in a 2 minute time-frame) and then tried breaking up the numerator and denominator. What do you recommend I do for similar questions like this where long division is not optimal and the numbers do not break up easily. I got it down to 17/90 but how am I supposed to know this represents .19?

Thanks


Yes, approximation is the best bet in such calculations.
10.2/54

Double of 54 is 108 so if you had 10.8/54, your answer would be .2
But you have a little less than 10.8. So your answer will be a little less than .2
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Re: Arithmetic operations of rational numbers [#permalink] New post 07 Feb 2014, 22:57
Why do I get the answer wrong when i do it the following way:

54/16.20= 3.333 ( price of each component in 54 piece box)
54/26.40= 2.045 (price of each component in 27 pieces box)
3.33-2.045=1.28

Where am I going wrong, please help...
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Re: Arithmetic operations of rational numbers [#permalink] New post 09 Feb 2014, 22:35
Expert's post
aleem681 wrote:
Why do I get the answer wrong when i do it the following way:

54/16.20= 3.333 ( price of each component in 54 piece box)
54/26.40= 2.045 (price of each component in 27 pieces box)
3.33-2.045=1.28

Where am I going wrong, please help...

Price of 54 components = $16.20
Price of one component = $16.20/54 (not the other way) = 0.3

Price of 27 components = $13.20
Price of one component = $13.20/27 = .49

Extra paid for each component = .49 - .3 = .19

(or use the method discussed above)
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Re: Arithmetic operations of rational numbers   [#permalink] 09 Feb 2014, 22:35
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