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

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

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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
[Reveal] Spoiler: OA

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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]

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Bunuel wrote:
Last week Jack worked 70 hours and earned $ 1,260. If he earned his regular hourly wage for the first 40 hours worked, 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


Is the question complete ? Shouldn't there be X times ?

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New post 26 Sep 2016, 08:44
Senthil1981 wrote:
Bunuel wrote:
Last week Jack worked 70 hours and earned $ 1,260. If he earned his regular hourly wage for the first 40 hours worked, 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


Is the question complete ? Shouldn't there be X times ?


Edited. Thank you for noticing.
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]

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New post 26 Sep 2016, 09:24
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)


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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]

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New post 26 Sep 2016, 10:03
Bunuel wrote:
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


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

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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]

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New post 26 Sep 2016, 10:36
Bunuel wrote:
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


Let Regular wages be " r "

Quote:
he earned his regular hourly wage for the first 40 hours worked,


So, wages for 40 Hrs is 40r

Quote:
3/2 times his regular hourly wage for the next 20 hours worked


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

Quote:
2 times his regular hourly wage for the remaining 10 hours worked


So, wages for 10 Hrs is 10*2r = 20r
Quote:
Jack worked 70 hours and earned $ 1,260.


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

Or, 90r = $ 1,260

Or, r = $ 14

Hence answer will be (B) $ 14

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New post 26 Sep 2016, 21:16
40x+30x+20x = 1260 =? 9x = 126

x = 14 $ Option B

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

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Bunuel wrote
Quote:
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 wrote:
Hi, Can somebody solve this question backward by considering answer choices.

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?

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