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Word Problem Mgmat

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Word Problem Mgmat [#permalink] New post 13 Jun 2010, 01:12
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A store sells erasers for $.23 each and pencils for $.11 each. IF Jessica buys both erasers and pencils from the store for a total of $1.70, what number of erasers and pencils did she buy.

This is from Mgmat Word translation book however will a problem like this ever asked to be solved or just DS. Either way is there any easy way to solve this? The book explanantion is just very long and not really practical.

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Dev
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Re: Word Problem Mgmat [#permalink] New post 13 Jun 2010, 06:05
We have the translated equation:

0.23e + 0.11p = 1.70
Multiply throughout by 100

23e + 11p = 170, where e and p are positive integers.

Now, this is a problem in which we have an equation in 2 variables, but both variables can only take integer values.

Remember this rule: For such problems, there exists only one possible solution for each of the variables if the LCM of the coefficients of each variable + the lower coefficient is greater than the RHS of the equation. So in DS if this is violated, you cannot find a solution.

Manhattan's method to solve this problem is actually quite cool, I would recommend you understand it in case this pops up in a PS though that's unlikely.
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Re: Word Problem Mgmat [#permalink] New post 13 Jun 2010, 09:53
Actually your right. The book gives the best method.

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Re: Word Problem Mgmat [#permalink] New post 15 Jun 2010, 08:44
go from answer choice..plug in method will be useful here
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Re: Word Problem Mgmat [#permalink] New post 15 Jun 2010, 11:10
jeeyo wrote:
A store sells erasers for $.23 each and pencils for $.11 each. IF Jessica buys both erasers and pencils from the store for a total of $1.70, what number of erasers and pencils did she buy.

This is from Mgmat Word translation book however will a problem like this ever asked to be solved or just DS. Either way is there any easy way to solve this? The book explanantion is just very long and not really practical.

Thanks

Dev


I don't know if I'm right but it is it 10? (5 per item)?

I solved it this way: if we multiply by 100 -> 23E+11P=170. 170 is an even number so E&P must either BOTH be odd or both be even. Because if E is odd and P is even we have an O+E, which does not equal an even number so it cannot be 170.

After that I just picked numbers by thinking how close the result would be to 170. 5 seemed like a good starting point and it worked out... (You could easily have picked 6 and realized that 6 was too big and just worked down).

5*23+5*11 = 170. So it should be 10.
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Re: Word Problem Mgmat [#permalink] New post 15 Jun 2010, 12:11
It is 10. Solve for 5 in one answer and plug that into the other equation. Answer choice plug in makes the most sense if it were a PS. If not actually the DS on this would be a bit harder to solve. Thanks everyone.
Re: Word Problem Mgmat   [#permalink] 15 Jun 2010, 12:11
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