Question

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?

Answer 1

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.

Answer 2

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.