document.write( "Question 1196618: The total expenditure E of a household is partly constant and partly varies directly as the size S of the household.
\n" ); document.write( "(a) find the equation connecting E and S, if when E=300,S=5persons and E=400,S=6
\n" ); document.write( "(b) what is the total expenditure when the size of the household is 10persoms
\n" ); document.write( "(c) how many persons will consume a total expenditure of $600 \n" ); document.write( "

Algebra.Com's Answer #829630 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The total expenditure E of a household is partly constant and partly varies directly as the size S of the household.
\n" ); document.write( "(a) find the equation connecting E and S, if when E=300,S=5persons and E=400,S=6
\n" ); document.write( "(b) what is the total expenditure when the size of the household is 10persoms
\n" ); document.write( "(c) how many persons will consume a total expenditure of $600
\n" ); document.write( "

This is a LINEAR system.\r\n" );
document.write( "\r\n" );
document.write( "Let slope be m, and constant, b\r\n" );
document.write( "We then get: E = mS + b____300 = 5m + b ----- eq (i)\r\n" );
document.write( "             E = mS + b____400 = 6m + b ----- eq (ii) \r\n" );
document.write( "                           100 = m ----- Subtracting eq (i) from eq (ii)\r\n" );
document.write( "                           300 = 5(100) + b ---- Substituting 100 for m in eq (i)\r\n" );
document.write( "                     300 - 500 = b____- 200 = b\r\n" );
document.write( "\r\n" );
document.write( "   Linear equation: E = mS + b______E = 100S - 200\r\n" );
document.write( "                                    E = 100(10) - 200 --- Substituting 10 for S\r\n" );
document.write( "For 10 people, expenditure or E = 1,000 - 200 = $800\r\n" );
document.write( "\r\n" );
document.write( "   Linear equation: E = mS + b______E = 100S - 200\r\n" );
document.write( "                                  600 = 100S - 200 ------ Substituting 600 for E\r\n" );
document.write( "                            600 + 200 = 100S\r\n" );
document.write( "                                  800 = 100S\r\n" );
document.write( "Number of persons when expenditure is $600 or

\n" ); document.write( "

\n" );