document.write( "Question 399463: 10 times my age minus 5 times my brothers age is 100. 10 years ago the square of my age plus the square of my brothers age was also 100. How old is my brother now? \n" ); document.write( "
Algebra.Com's Answer #282978 by ankor@dixie-net.com(22740)\"\" \"About 
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10 times my age minus 5 times my brothers age is 100.
\n" ); document.write( "10a - 5b = 100
\n" ); document.write( "-5b = -10a + 100
\n" ); document.write( "Simplify, divide by -5
\n" ); document.write( "b = 2a - 20
\n" ); document.write( ":
\n" ); document.write( "10 years ago the square of my age plus the square of my brothers age was also 100.
\n" ); document.write( "(a-10)^2 + (b-10)^2 = 100
\n" ); document.write( "replace b with (2a-20)
\n" ); document.write( "(a-10)^2 + ((2a-20) - 10)^2 = 100
\n" ); document.write( "(a-10)^2 + (2a-30)^2 = 100
\n" ); document.write( "FOIL
\n" ); document.write( "a^2 - 20a + 100 + 4a^2 - 120a + 900 = 100
\n" ); document.write( "Combine like terms
\n" ); document.write( "a^2 + 4a^2 - 20a - 120a + 100 + 900 = 100
\n" ); document.write( "5a^2 - 140a + 900 = 0
\n" ); document.write( "simplify, divide by 5
\n" ); document.write( "a^2 - 28a + 180 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(a-18)(a-10) = 0
\n" ); document.write( "a = 18
\n" ); document.write( "a = 10
\n" ); document.write( "Only a = 18 yrs for your age would work here
\n" ); document.write( ":
\n" ); document.write( "Find b
\n" ); document.write( "b = 2a - 20
\n" ); document.write( "b = 2(18) - 20
\n" ); document.write( "b = 16 yrs is the brother's age
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution in the 2nd equation
\n" ); document.write( "(18-10)^2 + (16-10)^2 =
\n" ); document.write( "8^2 + 6^2 = 100
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