document.write( "Question 1206529: a survey of 220 families showed that: 63 had a dog; 64 had a cat; 28 had a dog and a cat; 84 neither had a cat nor a dog and in addition did not have a parakeet; 6 had a cat, a dog and a parakeet. how many families had a parakeet only? \n" ); document.write( "

Algebra.Com's Answer #844073 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Use this Venn diagram:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We want to find y=?\r\n" );
document.write( "\r\n" );
document.write( "a survey of 220 families showed that: \r\n" );
document.write( "s+t+u+v+w+x+y+z=220\r\n" );
document.write( "63 had a dog; \r\n" );
document.write( "s+t+v+w=63\r\n" );
document.write( "64 had a cat;\r\n" );
document.write( "t+u+w+x=64 \r\n" );
document.write( "28 had a dog and a cat; \r\n" );
document.write( "t+w=28\r\n" );
document.write( "84 neither had a cat nor a dog and in addition did not have a parakeet; \r\n" );
document.write( "z=84\r\n" );
document.write( "6 had a cat, a dog and a parakeet. \r\n" );
document.write( "w=6\r\n" );
document.write( "\r\n" );
document.write( "how many families had a parakeet only?  That's y.\r\n" );
document.write( "\r\n" );
document.write( "     s t u v w x y z\r\n" );
document.write( "     | | | | | | | |\r\n" );
document.write( "(1)  s+t+u+v+w+x+y+z=220\r\n" );
document.write( "(2)  s+t  +v+w      = 63\r\n" );
document.write( "(3)    t+u  +w+x    = 64\r\n" );
document.write( "(4)    t    +w      = 28\r\n" );
document.write( "(5)                z= 84\r\n" );
document.write( "(6)          w      =  6\r\n" );
document.write( "\r\n" );
document.write( "Substitute w=6 in eq. (4) to get t=22\r\n" );
document.write( "Substitute t=22, w=6, z=84 in the first three \r\n" );
document.write( "equations and simplify:\r\n" );
document.write( "\r\n" );
document.write( "     s t u v w x y z\r\n" );
document.write( "     | | | | | | | |\r\n" );
document.write( "(1)  s  +u+v  +x+y   =108\r\n" );
document.write( "(2)  s    +v         = 35\r\n" );
document.write( "(3)      u    +x     = 36\r\n" );
document.write( "\r\n" );
document.write( "Subtract eqs. (2) and (3) from eq. (1) \r\n" );
document.write( "\r\n" );
document.write( "and get y = 37\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );