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Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour...

Expert replies
by swerve » Thu Mar 19, 2020 10:46 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty

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. 35
B. 36
C. 37
D. 38
E. 39

The OA is D

Source: Official Guide
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Source: — Problem Solving |

Harry is paid 30x + ( 15x * number of additional hours )
James is paid 40x + ( 2x * number of additional hours )

James worked a total of 41 hours hence he was paid 40x + ( 2x * 1 hour ) = 40x + 2x = 42x
Harry and James were paid the same amount last week
Let Harry's additional hours = y

James payment = Harry's payment
42x = 30x + 1.5xy
42x - 30x = 1.5xy
$$\frac{12x}{1.5x}=y$$
$$y=8$$

Harry worked for the first 30 hours and an additional 8 hours = 30 + 8 = 38 hours
Answer = D
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swerve wrote:
Thu Mar 19, 2020 10:46 am
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. 35
B. 36
C. 37
D. 38
E. 39

The OA is D

Source: Official Guide
Last week, James worked a total of 41 hours, and thus he earned 40x + 2x = 42x dollars. We can let h = the total number of hours Harry worked last week and create the equation:

30x + 1.5x(h - 30) = 42x

30x + 1.5xh - 45x = 42x

1.5xh - 15x = 42x

1.5xh = 57x

1.5h = 57

h = 57/1.5 = 38

Answer: D

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