MATH SOLVE

4 months ago

Q:
# The local animal shelter throws a dog-themed party. Humans, h, and dogs, d are both invited. The event space imposes two restrictions on the party: there can only be 120 dogs and humans combined, and, to keep things manageable, there must be 1 human to every 3 dogs. This situation can be represented by a system of two linear equations. One of these equations is given. Write the second equation in the box.d/3=h

Accepted Solution

A:

Answer:The system of equations can be expressed like[tex]\left\{\begin{matrix}h+d=120\\ 3h-d=0\end{matrix}\right.[/tex]Step-by-step explanation:System of Two Linear EquationsIt refers to situations where conditions are given in the form[tex]\left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]Where x and y are the unknown variables and a,b,c,d,e,f are known constantsThe problem describes a situation where one event space imposes two restrictions on a dog-themed party. The first one is there can only be 120 dogs and humans combined. Being h the number of humans, and d the number of dogs, then[tex]h+d=120[/tex]The other condition is there must be 1 human to every 3 dogs, we can model it by[tex]d=3h[/tex]Rearranging:[tex]3h-d=0[/tex]The system of equations can be expressed like[tex]\left\{\begin{matrix}h+d=120\\ 3h-d=0\end{matrix}\right.[/tex]Note: The solution of the system is h=30 humans and d=90 dogs