Question

Read a system of equations to describe the situation below solve using illumination and fill in the blanks

Answer 1

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