Question 1043527
WHAT WE KNOW:
{{{E}}}= government annual expenditure during each year of the 3-year boom (in millions of dollars).
{{{R}}}= government annual revenue during each year of the 3-year boom (in millions of dollars).
They tell us that {{{R-E=15}}} , so {{{R=E+15}}} .
That means that by the end of the 3-year boom,
The government has a nice {{{3*15=45}}} million dollars surplus saved for a rainy day.
{{{R-40=E+15-40=E-25}}}= the economist-predicted annual revenue for the next 5 years (in millions of dollars).
 
WHAT WE THINK:
Let us plan what the expenditure will be for the next 5 years.
(We will make it the same amount each year).
Obviously the annual expenditure needs to be less for the next 5 years.
Lets budget the smaller amount {{{B}}} to be the annual expenditure for each of the next 5 (lean) years.
Over the next 5 (lean) years the annual expenditure will be {{{B}}} million dollars,
and the total expenditure (in millions of dollars) will be {{{5B}}} .
At the same time (in millions of dollars), the annual revenue will be {{{E-25}}} ,
and the total revenue will be {{{5(E-25)}}} .
To have a balanced budget, the total revenue for the 5 lean years plus the saving from the boom years must equal the total expenditure for the 5 lean years.
So, our new equation is
{{{5(E-25)+45=5B}}} .
 
SOLVING THE EQUATION:
{{{5(E-25)+45=5B}}}
{{{5E-125+45=5B}}}
{{{5E-80=5B}}}
{{{5E-5B=80}}}
{{{5(E-B)=80}}}
{{{E-B=80/5}}}
{{{E-B=highlight(16)}}} .
That is (in millions of dollars) the difference between what the government was spending each year during the boom, {{{E}}} ,
and what the government can afford to spend, {{{B}}} , during each of the next 5 lean years.
Over the next 5 lean years the government's annual expenditure must be {{{B=E-16}}} ,
{{{highlight(16)}}} million dollars less than it was during the boom years.