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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?

Respuesta :

olemakpadu
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)
-
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.
meerkat18
Given:
4 shirts, 4 pairs of trousers , and 2 hats is    $560
9 shirts, 9 pairs of trousers , and 6 hats is $1,290

1) Let x be the price of 1 shirt
     Let y be the price of 1 pair of trousers
     Let z be the price of 1 hat

2) 4x + 4y + 2z =    560
3) 9x + 9y + 6z = 1,290

4) (9x + 9y + 6z) / 3 = 1,290 / 3
      3x + 3y + 2z = 430

5) 
   4x + 4y + 2z = 560
- (3x + 3y + 2z = 430)
     x  + y            = 130

6) 3(x+y) + 2z = 430 
     3(130) + 2z = 430
     390 + 2z = 430
                2z = 430 - 390
                2z = 40
                  z = 40/2
                  z = 20

7) x = price of 1 shirt; y = price of 1 pair of trousers ; z = price of 1hat
     x + y = 130 ; z = 20
     130 + 20 = 150

The price of 1 shirt, 1 pair of trousers, and 1 hat is $150.

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