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Algebra Word Problem - Problem Solving

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Algebra Word Problem - Problem Solving

by alexdu » Thu Aug 25, 2011 10:39 am
I'm working on a word problem that I'm not entirely sure how to solve. Any help regarding how to approach this problem would be greatly appreciated!

1. Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?

A). 34
B). 31
C). 14
D). 11
E). 7
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by BenchPrepGURU » Thu Aug 25, 2011 1:34 pm
1. Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?

A). 34
B). 31
C). 14
D). 11
E). 7

There are two equally valid ways to do this: the real math way, and the test prep way. I'll do them both. You should pick whichever way appeal to you - the admissions committee will never know. Just based on the numbers, I don't think the answer is one of the choices, but let's see:

Real Math:
James was paid x(40) + 2x(1) = 42x
Harry gets paid x(30) + 1.5x(h - 30) where h is the number of hours worked and h is greater than 30. So we need to set the two equations equal and solve for h.

42x = 30x + 1.5xh - 45x = 1.5xh - 15x
42x = 1.5xh - 15x (add 15x to both sides)
57x = 1.5xh (divide both sides by 1.5x)
38 = h

Test Prep Math: Pick an x. I pick $1/hr to make things easy.
James got 42 dollars.
Harry will get 30 + 1.5k where k is the number of hours over 30 he worked.
Set them equal
42 = 30 + 1.5k (subtract 30 from both sides)
12 = 1.5k (divide both sides by 1.5)
8 = k
So we add this to 30 to get Harry's total hours. 38.

As I suspected, the answer is not one of the choices. Where did you get this question?

As a follow up question, if Harry and James received the same pay for a certain week, and they worked the same number of hours for that week, and Harry worked more than 30 hours, how many hours did each man work?
60

BenchPrepGURU
benchprep.com
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by alexdu » Fri Aug 26, 2011 11:04 am
BenchPrepGURU wrote:1. Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?

A). 34
B). 31
C). 14
D). 11
E). 7

There are two equally valid ways to do this: the real math way, and the test prep way. I'll do them both. You should pick whichever way appeal to you - the admissions committee will never know. Just based on the numbers, I don't think the answer is one of the choices, but let's see:

Real Math:
James was paid x(40) + 2x(1) = 42x
Harry gets paid x(30) + 1.5x(h - 30) where h is the number of hours worked and h is greater than 30. So we need to set the two equations equal and solve for h.

42x = 30x + 1.5xh - 45x = 1.5xh - 15x
42x = 1.5xh - 15x (add 15x to both sides)
57x = 1.5xh (divide both sides by 1.5x)
38 = h

Test Prep Math: Pick an x. I pick $1/hr to make things easy.
James got 42 dollars.
Harry will get 30 + 1.5k where k is the number of hours over 30 he worked.
Set them equal
42 = 30 + 1.5k (subtract 30 from both sides)
12 = 1.5k (divide both sides by 1.5)
8 = k
So we add this to 30 to get Harry's total hours. 38.

As I suspected, the answer is not one of the choices. Where did you get this question?

As a follow up question, if Harry and James received the same pay for a certain week, and they worked the same number of hours for that week, and Harry worked more than 30 hours, how many hours did each man work?
60

BenchPrepGURU
benchprep.com
Thanks for your response! I apologize, I inadvertently copied the answers for the question above it.

The actual answer choices are:
A. 35
B. 36
C. 37
D. 38
E. 39
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