Respuesta :
Answer:
D) 11/3
Step-by-step 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 [tex]11x[/tex].
Money donated in 11 months would be [tex]\frac{11x}{10}[/tex].
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 [tex]Nx[/tex].
Money donated in December would be [tex]\frac{Nx}{5}[/tex].
The worker's charitable contributions totaled one-eighth of his earnings for the entire year that is [tex]\frac{1}{8}\cdot (11x+Nx)[/tex].
[tex]\frac{11x}{10}+\frac{Nx}{5}=\frac{1}{8}\cdot (11x+Nx)[/tex]
Dividing whole equation by x, we will get:
[tex]\frac{11x}{10x}+\frac{Nx}{5x}=\frac{1}{8x}\cdot x(11+N)[/tex]
[tex]\frac{11}{10}+\frac{N}{5}=\frac{1}{8}\cdot (11+N)[/tex]
[tex]\frac{11}{10}+\frac{N}{5}=\frac{11}{8}+\frac{N}{8}[/tex]
Combine like terms:
[tex]\frac{N}{5}-\frac{N}{8}=\frac{11}{8}-\frac{11}{10}[/tex]
[tex]\frac{N}{5}*40-\frac{N}{8}*40=\frac{11}{8}*40-\frac{11}{10}*40[/tex]
[tex]8N-5N=11*5-11*4[/tex]
[tex]3N=55-44[/tex]
[tex]3N=11[/tex]
[tex]\frac{3N}{3}=\frac{11}{3}\\\\N=\frac{11}{3}[/tex]
Therefore, the value of N is 11/3 and option D is the correct choice.
