Abox of wood pieces contains wood cut into triangular, square, and
pentagonal shapes. there are 80 pieces of wood in the box, and the pieces
have a total of 290 sides. if there are 10 more triangular pieces than square
pieces, find the number of pieces of wood of each shape in the box.

There are 30 square pieces, 40 triangular pieces and 10 pentagonal pieces.

Step-by-step explanation:

Let x be the number of square pieces. If there are 10 more triangular pieces than square pieces, then there are (x + 10) triangular pieces. Let y be the number of pentagonal pieces.

1. There are 80 pieces of wood in the box, then

(x + 10) + x + y = 80

2. There are

So,

3(x+10)+4x+5y=290

You get the system of two equations:

From the first equation,

Substitute it into the second equation

Hence, there are 30 square pieces, 40 triangular pieces and 10 pentagonal pieces.