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A shop sells a party hat at x dollars and a mask y dollars. On a particular morning, 3 hats and 4 mask were sold for $27. In the afternoon, 3 hats and 6 mask were sold for $33. Find the cost of each hat and each mask.

Answer :

TaeKwonDoIsDead

Answer:

Each hat cost = $5

Each mask cost = $3

Step-by-step explanation:

Hat = x dollars

Mask = y dollars

Now,

3 hat and 4 mask sold = $27

We can write:

3x + 4y = 27

Then,

3 hat and 6 mask sold = $33

We can write:

3x + 6y = 33

Adding 2nd equation with (-1 times 1st equation) gives us:

3x + 6y = 33

-1 * (3x + 4y = 27)

-------------------------

3x + 6y = 33

-3x -4y = -27

-------------------

2y = 6

y = 6/2

y = 3

Now we replace y = 3 into 1st equation and solve for x:

3x + 4y = 27

3x + 4(3) = 27

3x + 12 = 27

3x = 15

x = 15/3

x = 5

Each hat cost = $5

Each mask cost = $3

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