A polyhedron consists of faces only of squares and equilateral triangles. Given that it has $38$ faces and $60$ edges, find the ratio of square faces to triangular faces.
What I tried so far:
I let $x$ be the number of squares and $y$ be the number of triangles. Then we know that $x+y=38$. However, I am having trouble using $x$ and $y$ to relate it to the $60$ since it is harder to visualize.
Can anybody help?
Note that each edge of the polyhedron is connected to exactly $2$ faces. Since triangles have $3$ edges and squares have $4$ edges, then $4x+3y=2\times 60$, which together with $x+y=38$ implies that $x=6$ and $y=32$.