In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?

Let x = shirts, y = trousers, z = hats

Forming Equation 1

4x+4y+2z = 560

Simplifying it to,

2x + 2y + z = 280

Forming Equation 2

9x + 9y + 6z = 1290

Simpifying it to,

3x + 3y + 2z = 430

(1) 2x + 2y + z = 280

(2) 3x + 3y + 2z = 430

Doing (2) - (1)

3x + 3y + 2z = 430

2x + 2y + z = 280

Answer is

x + y + z = 150