Last week Jack worked 70 hours and earned $ 1,260. If he earned his re

Question

Last week Jack worked 70 hours and earned $ 1,260. If he earned his regular hourly wage for the first 40 hours worked, 3/2 times his regular hourly wage for the next 20 hours worked, and 2 times his regular hourly wage for the remaining 10 hours worked, what was his regular hourly wage?

A. $ 7.00
B. $ 14.00
C. $ 18.00
D. $ 22.00
E. $ 31.50

Saumya2403

Hi, Can somebody solve this question backward by considering answer choices.

A. $ 7.00
B. $ 14.00 
C. $ 18.00 
D. $ 22.00 
E. $ 31.50

TheOutlawTorn · Accepted Answer

Let hourly wage be x $/hr
Then : 
Wage for First 40hrs = x*40 $
Wage for next 20hrs = 1.5*x*20 $ (3/2 times hourly wage for next 20hrs)
Wage for remaining 10hrs = 2*x*10 (2 times hourly age for remaining 10 hours)

Adding them will be equal to total money earned => 90*x = 1260 $ 
Therefore x = 14 $/hr  Answer (B)

Senthil1981 · Answer

Let  x  be the hourly wage, so  40 * x + 20 * 1.5 * x + 10 * 2 * x = 1,260 
solve for  x  and it's B

Abhishek009 · Answer

Let Regular wages be " r "

So,  wages for 40 Hrs is 40r

So,  wages for 20 Hrs is   20 r \frac{3}{2}  =  30r

So,  wages for 10 Hrs is 10*2r  =  20r

So, 40r + 20r +30r = $ 1,260

Or, 90r = $ 1,260

Or, r = $ 14
 
 Hence answer will be (B) $ 14

deepthit · Answer

40x+30x+20x = 1260 =? 9x = 126

x = 14 $ Option B

Saumya2403 · Answer

Hi, Can somebody solve this question backward by considering answer choices.

generis · Answer

Bunuel  wrote
 
 Saumya2403  : Sure.

Start with C. Answer choices' numbers are in ascending order, we'll get a benchmark, and C is a round number. Answer C says  regular wage  is $ 18.00  per hour

If $ 18.00 is Jack's regular wage per hour:

1. For first block of 40 hours he earns the regular wage:

$18/hour * 40 hrs = $720

2. For the second block of 20 hours he earns "3/2 times his regular hourly wage":

\frac{3}{2}  * $18 = $27 per hour for the second block of 20 hours
 
$27/hour * 20 hrs = $540

3. For the final block of 10 hours he earns two times his regular hourly wage:

2 * $18 = $36 per hour for the final block of 10 hours
 
$36/hour * 10 hrs = $360

4. Add the totals for each time block to get total amount of money earned, which prompt says is $1,260.

$720 + $540 + $360 = $1,620. Not a match.

So $18.00 an hour as regular hourly wage is too high. Because D and E are even higher, eliminate C, D, and E

Answer A would be a drastic decrease per hour. Try B = $14.00 an hour for regular wage

1. First 40 hours at regular wage:

$14/hr * 40 hrs = $560

2. Second block of 20 hours at  \frac{3}{2}  times regular wage:

\frac{3}{2}  * $14 = $21/hr

($21/hr * 20 hrs) = $420

3. Final block of 10 hours at 2 times regular wage:

$14 * 2 = $28/hr

($28/hr * 10 hrs) = $280

Add the money totals for the three blocks of time: $560 + 420 + $280 = $1,260. Correct.

Answer B

Does that help?

UncleFrodo · Answer

Well, according to the task answer should be A ($7) and not B ($14). 
The question in the task is "what was his regular hourly wage" ? 
Regular hourly wage Jack got for regular working time per week - 40 hours. Next 20 hours and 10 hours are extra time and this time paid with coefficient. If we have a question like "what was his hourly wage for this week" - than the answer B will be correct.

generis · Answer

UncleFrodo  , could you elaborate? I do not understand what you are saying.

I do not see ambiguity in the question's language, if that is the issue.

Mathematically, I do not see how the regular hourly wage could be $7, if that is the issue.

Salsanousi · Answer

Let his regular hourly wage be x

We know he earned x for 40 hours = 40x

then he earned 3/2 times his regular hourly wage for 20 hours this means 3/2 * x *20 = 30x

then he earned 2 times his regular hourly wage for 10 hours this means 2 * x * 10 = 20x

adding them up we have 90x = 1,260

x = 14

tomvg · Answer

You can answer this question without necessarily using the whole calculation, but by looking at the answers and using the average amount earned.

Jack earned: 1260 / 70 = 18.00 dollars per hour, including all the extra rates.

So we can already eliminate answers (D) and (E), but also (C), as he certainly did not earn 18.00 as his regular rate.

Now we are left with answers (A) and (B). If we would take (A) = 7.00 per hour, that means Jack would have earned 14.00 for 10 hours. Which is still less than 18.00, which was the average earned. So we can also eliminate answer choice (A). And therefore (B) is what is left.

Ross7it · Answer

I used the same approach to solve this task.

The right answer should be less than 18 dollars.

P.S. This is the right approach to think and to answer the question having a 2 minutes deadline ...

MHIKER · Answer

Let the hourly wage is x
40x+20*1.5x+10x=1260
40x+30x+10x=1260
90x=1260
x=14
The hourly wage is 14
Answer B

naveeng15 · Answer

let x be regular wage

40x+20*2/3x+10*2x=1260
x=14

kokus · Answer

With all the overtime Jack worked 70h and earned $1260. Hence, he earned a combined hourly average rate of $18. Hence, directly C,D and E can be discarded since the standard rate must be less than $18.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Last week Jack worked 70 hours and earned $ 1,260. If he earned his re

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Last week Jack worked 70 hours and earned $ 1,260. If he earned his re

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards