Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra

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Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47

CareerGeek · Answer

For 40 hours, Salary = $20
—> Salary for 1 hour =  \frac{ 20}{40} = $ 0.5

salary per hour after 40 hours = 1/6 more tuan normal salary = 7/6th of 0.5 =  \frac{ 7}{6 }*0.5 = $\frac{ 7}{12 }

Let the number of hours worked beyond 40 =   x 
—> Overtime salary earned =   23.5 - 20 = 3.5  
—>  \frac{ 7}{12}* x = 3.5  
—>   x = 3.5* \frac{ 12}{7 } = 6   hours

So, total hours worked = 40 + 6 = 46

Option D

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Leadership · Answer

We know 40 hours = $20 ... overtime earned - $23.5 - $20 = $3.5
1 hour = $  \frac{20}{40}  = $0.5

Overtime - Salary/hr after 40 hours = 1/6 times the normal salary -  1 + \frac{1}{6} = \frac{7}{6} 
We can writes as -  \frac{7}{6} * 0.5  =  \frac{3.5}{6}

Let the number of hours worked after 40 hours as x and we already know that overtime earned is $3.5
 \frac{3.5 * x}{6 } = 3.5 
x=6

Total time - normal + overtime - 40 + 6 = 46

'D' is the winner

Archit3110 · Answer

gross wage per 40 hour week = 20$ ; per hour earning ; 20/40 ; .5 $
and overtime ; .5*1/6 ; .083 ; $.583 
so as to earn $23.5 ; i.e more than $3.5 than her usual time Blake would have to work ; 
3.5/.583 ; ~ 6 hrs more 
total hrs ; 46 hrs 
IMO D

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47

Raxit85 · Answer

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

(A) 43
(B) 44
(C) 45
(D) 46
(E) 47

$20/40 hrs = $ 0.5/hr. So, hourly rate is $0.5. 
I don't know to proceed traditionally but ill try from the options.
Let me try with 46 hrs. If blake's total extra required hours = 6, then he earns $3 extra, but here condition also applies. 
For 1 hr, 1/6*0.5 = 0.083, so for 6 hrs, 0.083*6 = 0.49 = 0.5.
So, 20 + 3 + 0.5 = 23.5.

Imo. D

Staphyk · Answer

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.
Goal: ?hrs — wk ——- 23.50

Let hrs =hours , wk= week
Started:40hrs ——— wk——— $20
Overtime wage = 7/6(Gross wage) = $23.33
Let’s find #of hrs $23.33 overtime
Started: 2hrs———- wk——— $1
Accumu. : 46.66hrs——wk—$23.33

Since we started with
40hrs———-wk———-$20.00
Overtime: 6.66hrs—-wk——$3.33
Overtime: 1hr —-wk——$0.50
Goal : (47)1hr—-wk—— $0.50(47)
Goal : 47hrs—wk—$23.50

Hit that E

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exc4libur · Answer

total wage in week = $20 for 40 hours
normal wage per hour = $20/40 = $1/2
overtime wage per hour = $1/2*7/6 = $7/12

normal time $20 = 40 hours
overtime $3.5 = $3.5/7/12 = 6 hours
total time = 46 hours

Ans (D)

freedom128 · Answer

Overtime rate = (7/6) * $20/40 =$7/12 per hour

Income = normal-hour + overtime
$23.5 = $20 + $(7/12)*h
h = 6 hours

Total hours per week= 40+h = 46 hours. 
 FINAL ANSWER IS (D)

eakabuah · Answer

Per hour rate for 40hr week = 20/5 = 0.5
Per hour rate for overtime = 7/6 * 1/2 = 7/12

Jake received 23.5 for a week, hence his total pay for overtime in the week = 3.5 = 7/2
Number of extra hours put in by Jake = (7/2)/(7/12) = (7*12)/(2*7) = 6 hours

So Jake had to work for 46 hours in order to earn $43.5

The answer is D.

lacktutor · Answer

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.

Gross wage —$20 for a 40 hour week
—> hourly —$ \frac{20}{40} = $0.5

Overtime — (\frac{1}{2})+ (\frac{1}{6})*(\frac{1}{2})= \frac{1}{2}+ \frac{1}{12} =$ \frac{7}{12}  (hourly)

—> 23.5 —20 = $3.5 (for overtime paid) 
—>  \frac{3.5}{(7/12)}=( \frac{7}{2})* (\frac{12}{7}) = 6  hours

—> 40+ 6 = 46 hours (in total )

The answer is D
 
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Jawad001 · Answer

Given that, Time is 40 hours in a week
 Gross wage = $20

Gross wage per hour = 20/40 =1/2
Over time per hour = ½*(7/6) = 7/12
Now,
 20 + (x-40)*7/12 = 23.50
(x-40) * 7/12 = 3.5
x-40 = 3.5*(12/7)
x-40 = 6
x =46

Total number of hours = 46(D)

neha283 · Answer

40 hr -->gross is 20$
1 hr -->gross is 0.5$
Blake has to earn 23.5$ this week, means 3.5$ in overtime. 
overtime for 1 hour = 0.5 + 1/6*0.5 = 7/12
3.5 = 7/2 
so, if he works for 6 hours overtime, 7/12 * 6 = 7/2 = 3.5$ 
so, D. 46 is the answer

QuantMadeEasy · Answer

Blake's gross wage for a 40 hour week is $20. Overtime is paid at a rate of one-sixth more than the gross. Find the number of hours that he has to work in a week in order to earn a total of $23.50.
Hourly regular wage = $20/40 = $1/2
Hourly overtime wage = (7/6)(1/2) = 7/12
Total overtime eage = 3.50
Hence, (7/12)*x = 7/2
x = 6
Total number of hours = 40+6 = 46

D is correct

KarishmaB · Answer

Normal wage per hour = 20/40 = $0.50
To make an extra $3.50, he would need to work 7 regular hours. But this money was made from overtime hours in which every hour pays 1/6th of the salary extra. So he needs to work only 6 hrs to make what he earns in 7 regular hrs.
Hence he will work 40 + 6 = 46 hrs

Answer (D)

bumpbot · Answer

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Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra

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Blake's gross wage for a 40 hour week is $20. Overtime is paid at a ra

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