document.write( "Question 377710: 1.Tom, Linda and Alex have $120 dollars. Alex has the third of what Tom has and Linda has twice as much as Alex. How much money, in dollars, does Linda have?
\n" ); document.write( "2.What is the smallest positive value of x for which y = cos(3x) has a minimum value?
\n" ); document.write( "3.ABC is a right triangle such that the length of BC is 5 units. The legs have length x and 2x. Find x. \r
\n" ); document.write( "\n" ); document.write( "4.In the figure below, EB and FC are both perpendicular to AC and x is the length of AB. If the length of AC is 11, what is x? \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #268441 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Tom, Linda and Alex have $120 dollars. Alex has the third of what Tom has and Linda has twice as much as Alex. How much money, in dollars, does Linda have?
\n" ); document.write( "

\r\n" );
document.write( "This one almost sets itself up because the words correspond almost\r\n" );
document.write( "exactly with the algebraic equation.  Just interpret \"have\" and \"has\"\r\n" );
document.write( "as an equal sign \"=\", and \"of\" as \"times\" indicated by • , and \"twice as much\"\r\n" );
document.write( "as \"2 times\" or \" 2 • \".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "[Tom], [Linda] [and] Alex [have] [$120 dollars]\r\n" );
document.write( "  |       |      |    |     |          | \r\n" );
document.write( "  T   +   L      +    A     =         120   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "[Alex] [has] [a third] [of] [what Tom has] \r\n" );
document.write( "   |     |       |      |        |\r\n" );
document.write( "   A     =      1/3     •        T\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "[Linda] [has] [twice as much as] [Alex]\r\n" );
document.write( "  |       |         |       |          |\r\n" );
document.write( "  L       =         2       •         A\r\n" );
document.write( "\r\n" );
document.write( "Put those three equations together and\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Can you solve that system of equations?  You can simplify the middle one by\r\n" );
document.write( "multiplying both sides by 3 and having:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now substitute 3*A for T and 2*A for L in\r\n" );
document.write( "\r\n" );
document.write( " T  +  L  + A = 120\r\n" );
document.write( "3*A + 2*A + A = 120\r\n" );
document.write( "          6*A = 120\r\n" );
document.write( "            A = 20\r\n" );
document.write( "\r\n" );
document.write( "Then L = 2*A = 2*(20) = 40\r\n" );
document.write( "and  T = 3*A = 3*(20) = 60\r\n" );
document.write( "\r\n" );
document.write( "So Tom has $T or $60, Linda has $L or $40, and Alex had $20.\r\n" );
document.write( "\r\n" );
document.write( "Alex has $20, which is a third of the $60 that Tom has, and since Linda has\r\n" );
document.write( "$40, that is indeed twice as much as Alex had, only $20. The question asks: \r\n" );
document.write( "\"How much money, in dollars, does Linda have?\"\r\n" );
document.write( "\r\n" );
document.write( "And of course the answer is $40.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );