document.write( "Question 825132: [ A boy observed that twice his age is 5 more years than his older sister's. His sister observed that twice the square of her brother's age subtracted from the square of her age is 7 years. Find the difference in their ages. ] \n" ); document.write( "
Algebra.Com's Answer #497066 by TimothyLamb(4379)![]() ![]() You can put this solution on YOUR website! --- \n" ); document.write( "x = boy \n" ); document.write( "y = girl \n" ); document.write( "--- \n" ); document.write( "2x = y + 5 \n" ); document.write( "yy - 2xx = 7 \n" ); document.write( "--- \n" ); document.write( "y = 2x - 5 \n" ); document.write( "yy - 2xx = 7 \n" ); document.write( "(2x - 5)(2x - 5) - 2xx = 7 \n" ); document.write( "4xx - 20x + 25 - 2xx = 7 \n" ); document.write( "2xx - 20x + 18 = 0 \n" ); document.write( "--- \n" ); document.write( "the above quadratic equation is in standard form, with a=2, b=-20, and c=18 \n" ); document.write( "--- \n" ); document.write( "to solve the quadratic equation, by using the quadratic formula, copy and paste this: \n" ); document.write( "2 -20 18 \n" ); document.write( "into this solver: https://sooeet.com/math/quadratic-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "this quadratic has two real roots (the x-intercepts), which are: \n" ); document.write( "x = 9 \n" ); document.write( "x = 1 \n" ); document.write( "--- \n" ); document.write( "NOTE: \n" ); document.write( "y = 2x - 5 \n" ); document.write( "for root x=1 \n" ); document.write( "y = 2(1) - 5 \n" ); document.write( "y = -3 \n" ); document.write( "y (the girl's age) cannot be negative: \n" ); document.write( "the root x=1 does not fit this problem statement, so use the root x=9 \n" ); document.write( "--- \n" ); document.write( "solution: \n" ); document.write( "x = boy = 9 \n" ); document.write( "y = girl = 13 \n" ); document.write( "--- \n" ); document.write( "age difference: 4 \n" ); document.write( "--- \n" ); document.write( "Solve and graph linear equations: \n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve quadratic equations, quadratic formula: \n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve systems of linear equations up to 6-equations 6-variables: \n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php \n" ); document.write( " |