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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
:
Let x = no. of 2nd Lt
Let y = no. of 1st Lt
Let z = no. of Capt.
:
Write an equation for each phrase
:
"If the total nbr of 2nd lieutenants and 1st lieutenatns is 30,"
x + y = 30
:
"the total nbr of 2nd lieutenants and captains is 45,"
x + z = 45
:
"and the total nbr of 1st lieutenatns and captains is 35,"
z + y = 35
:
Subtract the 1st equation from the 2nd equation
x + z = 45
x + y = 30
---------------subtraction eliminates x
z - y = 15
:
Add to the 3rd equation
z - y = 15
z + y = 35
-------------adding eliminates y, find z
2z = 50
z = 25 capt
then
25 + y = 35
y = 35 - 25
y = 10 1st Lt
and
x + 10 = 30
x = 30 - 10
x = 20 2nd Lt
:
:
Confirm this with the 2nd equation: x + z = 45
20 + 25 = 45
:
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I forgot to note that they asked asked for the total number of officers
20 + 10 + 25 = 55 is the total number of officers
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