document.write( "Question 417582: At a mess night, there are only captains, 2nd lieutenants, and 1st lieutenants (sounds like a damn good time). If the total nbr of 2nd lieutenants and 1st lieutenatns is 30, the total nbr of 2nd lieutenants and captains is 45, and the total nbr of 1st lieutenatns and captains is 35, what is the total nbr of company grade officers (2ndLts, 1stLts, and Capts are company grade officers) at the mess night? \n" ); document.write( "
Algebra.Com's Answer #292437 by ankor@dixie-net.com(22740)\"\" \"About 
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If the total nbr of 2nd lieutenants and 1st lieutenatns is 30, the total nbr of
\n" ); document.write( " 2nd lieutenants and captains is 45, and the total nbr of 1st lieutenatns and
\n" ); document.write( " captains is 35, what is the total nbr of company grade officers (2ndLts, 1stLts,
\n" ); document.write( " and Capts are company grade officers) at the mess night?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of 2nd Lt
\n" ); document.write( "Let y = no. of 1st Lt
\n" ); document.write( "Let z = no. of Capt.
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each phrase
\n" ); document.write( ":
\n" ); document.write( "\"If the total nbr of 2nd lieutenants and 1st lieutenatns is 30,\"
\n" ); document.write( "x + y = 30
\n" ); document.write( ":
\n" ); document.write( "\"the total nbr of 2nd lieutenants and captains is 45,\"
\n" ); document.write( "x + z = 45
\n" ); document.write( ":
\n" ); document.write( "\"and the total nbr of 1st lieutenatns and captains is 35,\"
\n" ); document.write( "z + y = 35
\n" ); document.write( ":
\n" ); document.write( "Subtract the 1st equation from the 2nd equation
\n" ); document.write( "x + z = 45
\n" ); document.write( "x + y = 30
\n" ); document.write( "---------------subtraction eliminates x
\n" ); document.write( "z - y = 15
\n" ); document.write( ":
\n" ); document.write( "Add to the 3rd equation
\n" ); document.write( "z - y = 15
\n" ); document.write( "z + y = 35
\n" ); document.write( "-------------adding eliminates y, find z
\n" ); document.write( "2z = 50
\n" ); document.write( "z = 25 capt
\n" ); document.write( "then
\n" ); document.write( "25 + y = 35
\n" ); document.write( "y = 35 - 25
\n" ); document.write( "y = 10 1st Lt
\n" ); document.write( "and
\n" ); document.write( "x + 10 = 30
\n" ); document.write( "x = 30 - 10
\n" ); document.write( "x = 20 2nd Lt
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this with the 2nd equation: x + z = 45
\n" ); document.write( "20 + 25 = 45
\n" ); document.write( ":
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\n" ); document.write( "I forgot to note that they asked asked for the total number of officers
\n" ); document.write( "20 + 10 + 25 = 55 is the total number of officers \n" ); document.write( "
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