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?

Respuesta :

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:

[tex]\frac{9.45}{100}x[/tex]

This increase is added to the initial salary x:

[tex]x+\frac{9.45}{100}x=87,609.50[/tex]

Isolate x from the equation to find its value:

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

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

[tex]\text{ \$80,045.23}[/tex]