For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chumpkin hide

Respuesta :

Let x and y be the number of holes dug by the chipmunk and the squirrel, respectively.

Therefore, the number of hidden acorns by each animal is given by the equations below

[tex]\begin{gathered} a_{chipmunk}=3x \\ a_{squirrel}=4y \end{gathered}[/tex]

On the other hand, since the squirrel needed 4 fewer holes, and the number of hidden acorns is the same

[tex]\begin{gathered} y=x-4 \\ and \\ a_{chipmunk}=a_{squirrel} \end{gathered}[/tex]

Thus,

[tex]\begin{gathered} \Rightarrow3x=4y \\ \Rightarrow3x=4(x-4) \\ \Rightarrow3x=4x-16 \\ \Rightarrow x=16 \end{gathered}[/tex]

Hence,

[tex]\Rightarrow16*3=48[/tex]

The chipmunk hid 48 acorns.