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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]
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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Re: Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]
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40x+30x+20x = 1260 =? 9x = 126

x = 14 $ Option 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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Hi, Can somebody solve this question backward by considering answer choices.
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Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]
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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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Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]
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.
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Last week Jack worked 70 hours and earned $ 1,260. If he earned his re [#permalink]
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UncleFrodo wrote:
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.

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


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


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

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