Question

System of linear equations and inequalities.A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was $7500 after 4 years of service and $9000 after 10 years of service, what was his starting salary and what is the anual increment? Do you consider it a fair increment according to our present cost of life and inflation?

Answer 1

Given

his salary was $7500 after 4 years and $9000 after 10 years of service

Find

His starting salary and what is the annual increment

Explanation

Assume starting salary be Rs . x and the fixed increment be Rs. y

then , according to the question

salary after 4 years of service = x + 4y

salary after 10 years of service = x + 10y

so ,

equations are

x + 4y = 7500 ...............(1)

x + 10y = 9000 ........(2)

solve equation by subtracting 1 and 2 equation ,

$\begin{gathered} x+4y-x-10y=7500-9000 \\ -6y=-1500 \\ y=\frac{1500}{6} \\ y=250 \end{gathered}$

now substitute value of y in equation 1,

$\begin{gathered} x+4(250)=7500 \\ x+1000=7500 \\ x=6500 \end{gathered}$

Final Answer

Hence , his starting salary is Rs 6500 and fixed increment is Rs 250