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)\"\" \"About 
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( "
\n" );