A child's sorting game has 31 shapes. Each piece is either a triangle or a square. The shapes have a total of 111 sides. Build a system of equations that can be used to find how many of each shape is used in the game.

Question

doc.brown · Answer

Number of triangles = t
Number of squares = s
3 sides for each triangle = 3t
4 sides for each square = 4s
Your equations are:
$$t + s = 31$$$$3t + 4s = 111$$
Solve:
$$t + s = 31$$$$t = 31 - s$$
Substitute t in equation 2
$$3t + 4s = 111$$$$3(31 - s) + 4s = 111$$$$93 - 3s + 4s = 111$$$$4s - 3s = 111 - 93$$$$s = 18$$
$$t = 31 - s$$$$t = 31 - (18)$$$$t = 13$$
check
$$3t + 4s = 111$$$$3(13) + 4(18) = 111$$$$39 + 72 = 111$$$$111 = 111$$