Question

A set of triangular and square tiles contains 50 pieces and 170 sides. Write a system of equations to represent this situation. Then solve the system to determine how many triangular and how many square tiles there are.

Answer 1

`\left\{\begin{array}{l}x+y=50\\3x+4y=170\end{array}\right.`

30 triangular tiles and 20 square tiles

Explanation:

A triangular tile has three sides, a square tile has 4 sides.

Let x be the number of triangular tiles and y be the number of square tiles. A set of triangular and square tiles contains 50 pieces, then

x+y=50

There are 3x sides in all triangular tiles and 4y sides in all square tiles. The set of triangular and square tiles contains 170 sides, so

3x+4y=170.

Hence, the system of two equations is

`\left\{\begin{array}{l}x+y=50\\3x+4y=170\end{array}\right.`

From the first equation

`x=50-y`

Substitute it into the second equation:

`3(50-y)+4y=170\\ \\150-3y+4y=170\\ \\y=170-150\\ \\y=20`

Thus,

`x=50-20=30`