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 $1,290. what is the total cost of 1 shirt, 1 pair of trousers and 1 hat?

Let the cost of the shirt be represented with s.

Let the cost of the pair of trousers be represented with t.

Let the cost of the hat be represented with h.

4 shirts, 4 pairs of trousers, 2 hats = $560

Implies      4s + 4t  +  2h = 560.  Divide through by 2
                   2s + 2t  + h =  280(a)

9 shirts, 9 pairs of trousers, 6 hats = $1290

Implies      9s + 9t  +  6h = 1290. Divide through by 3
                   3s + 3t  + 2h = 430 (b)

Equation (b) -  (a)

3s + 3t  + 2h = 430 (b)
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2s + 2t  + h =  280(a)

s  +  t  +  h    =   150

From the resulting equation s  +  t  +  h    =   150, we can see that  1 shirt, 1 pair of trousers and 1 hat cost  $150.