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At a bakery, Tom normally earns x dollars per hour of the first n hour

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At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 22 Jan 2018, 23:24
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Difficulty:

  95% (hard)

Question Stats:

56% (02:42) correct 44% (03:09) wrong based on 81 sessions

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At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?

A. 7 : 10
B. 375 : 100
C. 100 : 375
D. 11 : 8
E. 8 : 11

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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 23 Jan 2018, 00:15
E

This question can easily be solved by assuming values.

Lets say tom earns 10$ per hour working for 8 hours normal time. his total earning is 80$.

Now wage for OT hours = 13.75$ per hour. this is to be equal to 80$ to make his income double.

Hence number of OT hours need to be worked is 80/13.75=35/6.

Hence ratio of OT hours to normal hours = 35/6/(8) = 8:11. option E
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At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 23 Jan 2018, 00:25
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Bunuel wrote:
At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?

A. 7 : 10
B. 375 : 100
C. 100 : 375
D. 11 : 8
E. 8 : 11


Let a be the number of extra hours, so as per the question \(nx + a(1.375x) = 2nx\)
\(n = 1.375a\) or \(a/n = 8/11\)
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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 18 Feb 2018, 07:04
Let \(t\) be the total hours that Tom worked in a day, of which \(n\) are regular hours and \(t-n\) are overtime hours. We are asked to find the ratio of \(\frac{(t-n)}{n}\) such that Tom's income is double.

So for Tom to earn the double of his regular rate, the number of hours that he has to work can be expressed as -
\(nx+1.375(t-n)x = 2nx\)
\(n+1.375(t-n) = 2n\)
\(1.375(t-n) = n\)
\(\frac{(t-n)}{n}=\frac{1}{1.375}=\frac{8}{11}\)


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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour [#permalink]

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New post 25 Feb 2018, 16:03
Hi All,

This question has a number of subtle 'hints' built into it (and the answer choices) that would help you to TEST VALUES. Most of the TESTs that you could do will involve fractions though (which is part of what makes this question harder than average). Here's how you could approach it:

We're told Tom gets paid $X per hour for each of the first N hours worked...
then Tom gets paid $1.375X per hour for each additional hour thereafter.

The first "hint" is that 0.375 = 3/8, so Tom gets paid (1 3/8)X for each overtime hour. This means that making X a multiple of 8 should help to simplify the math a bit.

We're then asked for the ratio of OVERTIME hours to REGULAR hours needed to DOUBLE his daily pay.

IF....
X = 8
N = 2
Tom earns $8(2 hours) = $16 of normal pay

(1 3/8)(8) = $11/hour for each overtime hour.

To DOUBLE his normal pay, the overtime pay must ALSO equal $16, so...

$11(Z overtime hours) = $16
Z = 16/11

So the ratio of overtime hours to regular hours is...

16/11: 2

This ratio needs to be "cleaned up" though, so let's multiply both sides by 11...

16: 22

And then reduce....

8:11

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Re: At a bakery, Tom normally earns x dollars per hour of the first n hour   [#permalink] 25 Feb 2018, 16:03
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