Answer: 275 adults and 130 children
Step-by-step explanation:
First, find the value of one variable by rearranging a equation:
[tex]a+c=405\\c=405-a[/tex]
Substitute it into the other equation and solve for a:
[tex]12a+5c=3950\\12a+5(405-a)=3950\\12a+2025-5a=3950\\12a-5a=3950-2025\\7a=1925\\a=\frac{1925}{7} =275[/tex]
Use the a-value to find b by substituting it into the rearranged equation:
[tex]c=405-a=405-275=130[/tex]
Therefore, the answer would be:
[tex]\left \{ {{a=275} \atop {c=130}} \right.[/tex]
