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A man starts his job with a certain monthlysalary and earns a fixed increment every year. If his salary was$7500 after 4 years of service and $9000 after 10 years ofservice, what was his starting salary and what is the annualincrement? Do you consider it a fair increment according to ourpresent cost of life and infletion?

A man starts his job with a certain monthlysalary and earns a fixed increment every year If his salary was7500 after 4 years of service and 9000 after 10 years class=

Respuesta :

Let starting salary = x

Increment every year = y

Therefore:

Salary after 4 years of service = x+4y

Salary after 10 years of service = x+10y

We have the equations:

[tex]\begin{gathered} x+4y=7500 \\ x+10y=9000 \end{gathered}[/tex]

Substracting equation 1 from equation 2, we get:

[tex]x+10y-(x+4y)=9000-7500[/tex]

Simplify:

[tex]\begin{gathered} x+10y-x-4y=1500 \\ 6y=1500 \\ Solve\text{ for y} \\ \frac{6y}{6}=\frac{1500}{6} \\ y=250 \end{gathered}[/tex]

Next, substitute y = 250 in the equation 1:

[tex]x+4(250)=7500[/tex]

And solve for x:

[tex]\begin{gathered} x+1000=7500 \\ x+1000-1000=7500-1000 \\ x=6500 \end{gathered}[/tex]

Answer:

Starting salary = $6500

Annual increment = $250

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