document.write( "Question 1043527: during a 3 years boom, a government experienced a budget surplus of 15 million dollars per year. a economist predicts that annual revenue will drop to 40 million dollars below current levels and remain at that level for the next 5 years. by how much must the government reduce expenditures yearly to maintain a balanced budget over this period? \n" ); document.write( "

Algebra.Com's Answer #659141 by KMST(5328) $\"\"$ $\"About$

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WHAT WE KNOW:
\n" ); document.write( " $\"E\"$ = government annual expenditure during each year of the 3-year boom (in millions of dollars).
\n" ); document.write( " $\"R\"$ = government annual revenue during each year of the 3-year boom (in millions of dollars).
\n" ); document.write( "They tell us that $\"R-E=15\"$ , so $\"R=E%2B15\"$ .
\n" ); document.write( "That means that by the end of the 3-year boom,
\n" ); document.write( "The government has a nice $\"3%2A15=45\"$ million dollars surplus saved for a rainy day.
\n" ); document.write( " $\"R-40=E%2B15-40=E-25\"$ = the economist-predicted annual revenue for the next 5 years (in millions of dollars).
\n" ); document.write( "
\n" ); document.write( "WHAT WE THINK:
\n" ); document.write( "Let us plan what the expenditure will be for the next 5 years.
\n" ); document.write( "(We will make it the same amount each year).
\n" ); document.write( "Obviously the annual expenditure needs to be less for the next 5 years.
\n" ); document.write( "Lets budget the smaller amount $\"B\"$ to be the annual expenditure for each of the next 5 (lean) years.
\n" ); document.write( "Over the next 5 (lean) years the annual expenditure will be $\"B\"$ million dollars,
\n" ); document.write( "and the total expenditure (in millions of dollars) will be $\"5B\"$ .
\n" ); document.write( "At the same time (in millions of dollars), the annual revenue will be $\"E-25\"$ ,
\n" ); document.write( "and the total revenue will be $\"5%28E-25%29\"$ .
\n" ); document.write( "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.
\n" ); document.write( "So, our new equation is
\n" ); document.write( " $\"5%28E-25%29%2B45=5B\"$ .
\n" ); document.write( "
\n" ); document.write( "SOLVING THE EQUATION:
\n" ); document.write( " $\"5%28E-25%29%2B45=5B\"$
\n" ); document.write( " $\"5E-125%2B45=5B\"$
\n" ); document.write( " $\"5E-80=5B\"$
\n" ); document.write( " $\"5E-5B=80\"$
\n" ); document.write( " $\"5%28E-B%29=80\"$
\n" ); document.write( " $\"E-B=80%2F5\"$
\n" ); document.write( " $\"E-B=highlight%2816%29\"$ .
\n" ); document.write( "That is (in millions of dollars) the difference between what the government was spending each year during the boom, $\"E\"$ ,
\n" ); document.write( "and what the government can afford to spend, $\"B\"$ , during each of the next 5 lean years.
\n" ); document.write( "Over the next 5 lean years the government's annual expenditure must be $\"B=E-16\"$ ,
\n" ); document.write( " $\"highlight%2816%29\"$ million dollars less than it was during the boom years. \n" ); document.write( "

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