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For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4

1 Answer

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Answer:

D) 11/3

Explanation:

Let x represent monthly salary.

We have been given that for each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity.

Salary earned in 11 months would be
11x.

Money donated in 11 months would be
(11x)/(10).

Further we are told that in December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity.

Salary for December would be
Nx.

Money donated in December would be
(Nx)/(5).

The worker's charitable contributions totaled one-eighth of his earnings for the entire year that is
(1)/(8)\cdot (11x+Nx).


(11x)/(10)+(Nx)/(5)=(1)/(8)\cdot (11x+Nx)

Dividing whole equation by x, we will get:


(11x)/(10x)+(Nx)/(5x)=(1)/(8x)\cdot x(11+N)


(11)/(10)+(N)/(5)=(1)/(8)\cdot (11+N)


(11)/(10)+(N)/(5)=(11)/(8)+(N)/(8)

Combine like terms:


(N)/(5)-(N)/(8)=(11)/(8)-(11)/(10)


(N)/(5)*40-(N)/(8)*40=(11)/(8)*40-(11)/(10)*40


8N-5N=11*5-11*4


3N=55-44


3N=11


(3N)/(3)=(11)/(3)\\\\N=(11)/(3)

Therefore, the value of N is 11/3 and option D is the correct choice.

User Leightski
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