There were 44 children, 43 adults and 77 seniors were at the local auto show.
Step-by-step explanation:
Cost of child admission = $7
Cost of adult admission = $12
Cost of senior admission = $9
Total people attended = 164
Total revenue generated = $1517
Raffle tickets filled = 120
Let,
Number of child tickets sold = x
Number of adult tickets sold = y
Number of senior tickets sold = z
According to given statement;
x+y+z=164 Eqn 1
y+z= 120 Eqn 2
7x+12y+9z=1517 Eqn 3
Putting y+z=120 from Eqn 2 in Eqn 1;
[tex]x+120=164\\x=164-120\\x=44[/tex]
Putting x=44 in Eqn 3
[tex]7(44)+12y+9z=1517\\308+12y+9z=1517\\12y+9z=1517-308\\12y+9z=1209\ \ \ \ Eqn\ 4[/tex]
Multiplying Eqn 2 by 12;
[tex]12(y+z=120)\\12y+12z=1440\ \ \ Eqn\ 5[/tex]
Subtracting Eqn 4 from Eqn 5
[tex](12y+12z)-(12y+9z)=1440-1209\\12y+12z-12y-9z=231\\3z=231[/tex]
Dividing both sides by 3
[tex]\frac{3z}{3}=\frac{231}{3}\\z=77[/tex]
Putting z=77 in Eqn 2
[tex]y+77=120\\y=120-77\\y=43[/tex]
There were 44 children, 43 adults and 77 seniors were at the local auto show.
Keywords: linear equation, addition
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