Question

Last year, John made $36,000 and payed 15% in federal taxes. This year he received a raise to $41,000. This moved him into a higher tax bracket, where he paid 25% in federal taxes. In which year did John earn more after taxes, and by how much? F Last year, by $150 G Last year, by $4,100 H This year, by $150 J This year, by $7,850​

Answer 1

well, let's take a looksie
hmmmm last year he paid 15% of 36000

`\begin{array}ll \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 36000}}{\left( \cfrac{15}{100} \right)36000}\implies 5400`

this year he's paying 25% of 41000

`\begin{array}c \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 41000}}{\left( \cfrac{25}{100} \right)41000}\implies 10250`

well, hmmm let's see

`\underset{this~year}{\stackrel{41000-10250}{\text{\LARGE 30750}}}~~ - ~~\underset{last~year}{\stackrel{36000-5400}{\text{\LARGE 30600}}}\implies \stackrel{by}{\text{\LARGE 150}}`