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Word Translation problem: bonus is given in a weird way

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Word Translation problem: bonus is given in a weird way [#permalink] New post 14 Jul 2013, 13:08
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Hi friends!

Im just about done with MGMATs foundations of math book, and in the end-of-chapter drills there is a question that reads like this:

Quote:
Arnaldo earns $11 for each ticket that he sells, and a bonus of $2 per ticket for each ticket he sells over 100. If Arnaldo was paid $2,400, how many tickets did he sell


As I interpret it:

Lets call the first 100 ticets t1, and all the additional past 100 we call t2.

He earns $11*t1 and "a bonus of $2 [per t2]". This, to me, reads as t2 = 11 + 2, since he (obviously) still earns the initial 11USD on top of the bonus amount. So in other words t2 = t1 + 2

So:

11*t1 + (11+2)*t1 = 2400 ---> 24*t1 = 2400 ----> t1 = 1000


According to the OA, this is wrong. Their reasoning is:

total ticets sold = t
Ticets sold beyond 100 = (t - 100)

And thus:

11t + 2(t - 100) = 2400 ---> 13t = 2600 ----> t = 200

But whats upp with 2(t - 100)?? As I interpret this... It means that "he only earns $2 for every ticket sold over 100" and I get that this reasoning is wrong but I need a much clearer and better explanation than the one given by the book. All help is greatly appreciated.
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Re: Word Translation problem: bonus is given in a weird way [#permalink] New post 14 Jul 2013, 13:28
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aeglorre wrote:
Hi friends!

Im just about done with MGMATs foundations of math book, and in the end-of-chapter drills there is a question that reads like this:

Quote:
Arnaldo earns $11 for each ticket that he sells, and a bonus of $2 per ticket for each ticket he sells over 100. If Arnaldo was paid $2,400, how many tickets did he sell


As I interpret it:

Lets call the first 100 ticets t1, and all the additional past 100 we call t2.

He earns $11*t1 and "a bonus of $2 [per t2]". This, to me, reads as t2 = 11 + 2, since he (obviously) still earns the initial 11USD on top of the bonus amount. So in other words t2 = t1 + 2

So:

11*t1 + (11+2)*t1 = 2400 ---> 24*t1 = 2400 ----> t1 = 1000


According to the OA, this is wrong. Their reasoning is:

total ticets sold = t
Ticets sold beyond 100 = (t - 100)

And thus:

11t + 2(t - 100) = 2400 ---> 13t = 2600 ----> t = 200

But whats upp with 2(t - 100)?? As I interpret this... It means that "he only earns $2 for every ticket sold over 100" and I get that this reasoning is wrong but I need a much clearer and better explanation than the one given by the book. All help is greatly appreciated.


Actually OE takes into account $11 earned over 100.

Total tickets sold = t.

For all t tickets he earns $11, so 11t.

Then we have t-100 tickets over 100. He earns $2 for each ticket over 100, so additional 2(t-100).

Total = 11t + 2(t - 100) = 2400 --> t = 200.

Hope it's clear.
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Comparing Two Similar Word Problems [#permalink] New post 10 Oct 2013, 15:19
Hello all, I have a question regarding two similar word problems and my approaches to solving them. It appears that one approach works for one and does not for the other.
The first problem is as follows:

Arnaldo earns $11 for each ticket that he sells, and a bonus of $2 per ticket for each ticket he sells over 100. If Arnaldo was paid $2,400, how many tickets did he sell?

My solution: 11x+2(x-100)=$2400, solve for x which equals 200 tickets

Question two is as follows:

Every week, Renee is paid $40 per hour for the first 40 hours she works and $80 per hour for each hour she works after 40 hours. If she earned $2,000 last week, how many hours did she work?

My solution: 40x+80(x-40)=$2,000, solve for x, which equals 43.333 hours (the correct answer is 45 hours)

My question is why does one approach work for one problem while it does not for the other? Or does it and my equations are flawed?

Thanks in advance!
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Re: Comparing Two Similar Word Problems [#permalink] New post 10 Oct 2013, 15:39
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lilmanmr wrote:
Hello all, I have a question regarding two similar word problems and my approaches to solving them. It appears that one approach works for one and does not for the other.
The first problem is as follows:

Arnaldo earns $11 for each ticket that he sells, and a bonus of $2 per ticket for each ticket he sells over 100. If Arnaldo was paid $2,400, how many tickets did he sell?

My solution: 11x+2(x-100)=$2400, solve for x which equals 200 tickets

Question two is as follows:

Every week, Renee is paid $40 per hour for the first 40 hours she works and $80 per hour for each hour she works after 40 hours. If she earned $2,000 last week, how many hours did she work?

My solution: 40x+80(x-40)=$2,000, solve for x, which equals 43.333 hours (the correct answer is 45 hours)



My question is why does one approach work for one problem while it does not for the other? Or does it and my equations are flawed?

Thanks in advance!


the second one should be : 40*40+80*(x-40)=2000, cuz we are told that the rate of $40 per hour is only applied to first 40 hours.
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Re: Comparing Two Similar Word Problems [#permalink] New post 10 Oct 2013, 16:21
Ah yes, that does make sense now doesn't it? Thank you for your help!
Re: Comparing Two Similar Word Problems   [#permalink] 10 Oct 2013, 16:21
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