document.write( "Question 1200103: Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts costs $15. If she bought a total of 7 shirts then how many of each kind did she buy \n" ); document.write( "
Algebra.Com's Answer #834123 by math_tutor2020(3816)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "x = number of fancy shirts \n" ); document.write( "7-x = number of plain shirts\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Total cost: \n" ); document.write( "fancy + plain = $131 \n" ); document.write( "28x + (105-15x) = 131 \n" ); document.write( "13x + 105 = 131 \n" ); document.write( "13x = 131 - 105 \n" ); document.write( "13x = 26 \n" ); document.write( "x = 26/13 \n" ); document.write( "x = 2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Fancy = x = 2 \n" ); document.write( "Plain = 7-x = 7-2 = 5\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Check: \n" ); document.write( "1 fancy shirt = $28 \n" ); document.write( "2 fancy shirts = 2*$28 = $56 \n" ); document.write( "1 plain shirt = $15 \n" ); document.write( "5 plain shirts = 5*$15 = $75 \n" ); document.write( "2 fancy + 5 plain = $56 + $75 = $131 total \n" ); document.write( "2 fancy + 5 plain = 7 shirts total \n" ); document.write( "The answers are confirmed.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-----------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Another approach:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let's say all 7 shirts were fancy. \n" ); document.write( "7*28 = 196 \n" ); document.write( "She would spend $196\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The gap from $131 to $196 is \n" ); document.write( "196-131 = 65 \n" ); document.write( "Her total cost needs to drop by $65 to get to $131\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Each time we subtract 1 fancy shirt, and add a plain shirt, we subtract a net cost of $13 (since -28+15 = -13) \n" ); document.write( "Then notice how 13 is a factor of 65 \n" ); document.write( "65 = 13*5 \n" ); document.write( "This tells us that we need to introduce 5 plain shirts\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The 7 fancy shirts will drop to 7-5 = 2 fancy shirts.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-----------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Another approach:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = number of fancy shirts \n" ); document.write( "y = number of plain shirts\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x+y = 7 ... shirt count equation \n" ); document.write( "28x+15y = 131 .... shirt cost equation\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Graph those two equations using something like Desmos or GeoGebra. Both are free.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The two equations intersect at (2,5) \n" ); document.write( "Meaning we have x = 2 fancy shirts and y = 5 plain shirts\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x+y = 7 in green \n" ); document.write( "28x+15y = 131 in blue\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-----------------------------------------------------\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answers: \n" ); document.write( "2 fancy and 5 plain \n" ); document.write( " \n" ); document.write( " |