Question

Nermal Kumar is a senior manager for Timber Eye Industries in California. After his annual performance review, he receives a merit raise of 7.25% and a cost-of-living increase of 2.2%. His annual salary after the increases was $87,609.50. What was Nermal's annual salary before the two increases took effect?

Answer 1

Let x be the initial salary before the two increases took effect.

Notice that a total increase of 7.25%+2.2%=9.45% was applied.

Express 9.45% of x by multiplying x times 9.45/100:

`(9.45)/(100)x`

This increase is added to the initial salary x:

`x+(9.45)/(100)x=87,609.50`

Isolate x from the equation to find its value:

`\begin{gathered} \Rightarrow x+0.0945x=87,609.50 \\ \Rightarrow(1+0.0945)x=87,609.50 \\ \Rightarrow1.0945x=87,609.50 \\ \Rightarrow x=(87,609.50)/(1.0945) \\ \Rightarrow x=80,045.23\ldots \end{gathered}`

Therefore, Nermal's annual salary before the two increases took place, was:

`\text{ \$80,045.23}`