document.write( "Question 1110439: Jack and Jill spent two weeks touring Boston, New York City, Philadelphia, and Washington D.C. They paid $120,$200,$80, and $100 per night respectively. Their total bill was $2020. The number of days spent in NYC was the same as the sum of the days spent in Boston and D.C. They spent three times as many days in NYC as they did in Philly. How many days did they stay in each city?
\n" );
document.write( "a) answer question using a combination of algebra and logic.
\n" );
document.write( "b) answer the question again using a 4x4 system of equations.\r
\n" );
document.write( "\n" );
document.write( "Does this mean there's another way to do this without a system of equations? That's the only way I can think of doing it. I just know that 120B+200N+80P+100W=2020. \n" );
document.write( "
Algebra.Com's Answer #725559 by ikleyn(52790)![]() ![]() You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " The usual practice in hotels is to pay for night.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " But, specially for the purpose of this problem, I will assume that they pay for each DAY and that the number of days was 14 (\"two weeks\" literally).\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Solution\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "Let P be the number of days in Philly.\r\n" ); document.write( "\r\n" ); document.write( "Then the number of days in NYC is 3P, from the condition.\r\n" ); document.write( "\r\n" ); document.write( "We also are given that the number of days in NYC, 3P, is equal to B + W.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "So we have\r\n" ); document.write( "\r\n" ); document.write( "P + 3P + (B + W) = 14, or, replacing B + W by \"3P\", \r\n" ); document.write( "\r\n" ); document.write( "P + 3P + 3P = 14,\r\n" ); document.write( "\r\n" ); document.write( "7P = 14 ====> P =\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "It is how my logic works. \n" ); document.write( "Still, it is not the final solution yet, but I just reduced the problem to the only 2 (two, TWO) unknowns B and W,\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and at this point, I an sure, now you are able to complete the solution WITHOUT MY HELP, \n" ); document.write( "using REMAINING CONDITION on the total cost.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |