Question 784742
${{{x}}}= previous job salary
${{{x-30600}}}= decrease in salary (pay cut as $ amount)
 
You can look at the calculations two ways:
 
THE SIMPLER WAY (no need to mention algebra; a fifth grader can do it):
Bradley may have compared the new salary to the old salary (dividing the new salary by the old one) and the result was {{{0.85=85/100="85 %"}}}.
That would have told him that the % pay cut was
100% - 85% = 15%
To reverse that calculation, you would start by
100% - 15% = 85% and that would tell you that Bradley is now making only 85% of the previous job salary.
As a fraction, 85% is {{{0.85=85/100="85 %"}}}.
The new salary is {{{0.85 =85/100}}} of the old one,meaning that it is
{{{"$"}}}{{{ 0.85*x}}}{{{"="}}}{{{"$"}}}{{{"30,600"}}}
Reversing that calculation,
{{{x=30600/0.85}}} --> {{{x=36000}}}
(Simple calculators that have a % key, use the number 0.85 when you enter 85%, so I enter 30600 ÷ 85 %, and I get 36000 without even touching the = key).
 
ANOTHER WAY OF LOOKING AT IT:
When calculating the percent pay cut, Bradley may have divided the $ amount of the pay cut by the old salary and the result was {{{0.15=15/100="15 %"}}}
{{{(x-30600)/x=0.15}}}
In solving that equation, you could multiply both sides of the equal sign times {{{x}}} and get an equivalent equation (as long as {{{x<>0}}}, which is true in this case).
{{{(x-30600)/x=0.15}}}-->{{{x-30600=0.15x}}}-->{{{x=0.15x+3060}}}-->{{{x-0.15x=30600}}}-->{{{1*x+0.15*x=30600}}}-->{{{(1-0.15)*x=30600}}}-->{{{0.85x=30600}}-->{{{0.85x/0.85=30600/0.85}}}-->{{{x=36000}}}
(I would write that skipping the steps than seem too obvious, but showing enough steps to satisfy the person who's reading it, or the teacher).