System of Equations
Let:
x = number of people that can be seated at a table
y = number of people that can be seated at a booth
The first plan consists of 23 tables and 10 booths and then 228 people could be seated, thus:
23x + 10y = 228
The second plan consists of 12 tables and 12 booths and that way 180 people could be seated, thus:
12x + 12y = 180
The method of elimination requires equating the coefficients of one variable and eliminating it by adding the equations.
Multiply the first equation by 12:
276x + 120y = 2736
Multiply the second equation by -23:
-276x - 276y = -4140
Add the last two equations (the variable x cancels out):
120y - 276y = 2736 - 4140
Simplifying:
-156y = -1404
Dividing by -156:
y = -1404/(-156)
y = 9
Substitute this value in the first equation:
23x + 10(9) = 228
Operate:
23x + 90 = 228
Subtract 90:
23x = 138
Divide by 23:
x = 138/23
x = 6
Every table can seat 6 people, and every booth can seat 9 people
-4 is also a geometric mean
if we consider a(first element in series)=1 and r(common ratio)=-4 then the series would be
1,-4,16,-64,256,…..,a(-4)^(n-1 )
where n is nth term
from this -4 would be the geometric mean if we consider -4 as common ratio .
If we consider 4 as common ratio then geometric mean should be 4
so you should mention whether common ratio >0 or not (r>0 or not) .
[without ‘r’ value you can’t solve the question but in general most of the teachers will consider r>0.]
So, -4 won’t be geometric mean of 1 & 16
A≈259.81in²
I hope this helped!!
6.4 - 2x - 6.63x = 610.5
subtract 6.4 from both sides
-2x -6.63x =604.1
collect like terms
-8.63x = 604.1
divide both sides by -8.63
x= -70
