Question

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

Answer 1

Cost of each hat: $5

Cost of each mask: $3

Explanation:

Let be "x" the cost in dollars of a party hat and "y" the cost in dollars of a mask.

Set up a System of equations using the information given in the exercise:

`\left \{ {{3x+4y=27} \atop {3x+6y=33}} \right.`

You can use the Elimination Method to solve this System of equations:

1. You can multiply the first equation by -1.

2. Then you must add the equations.

3. Solve for "y".

Then:

`\left \{ {{-3x-4y=-27} \atop {3x+6y=33}} \right.\\.....................\\2y=6\\\\y=(6)/(2)\\\\y=3`

4. Now you can substitute the value of "y" into any original equation.

5. Finally, solve for "x" in order to find its value.

Then:

`3x+4(3)=27\\\\3x=27-12\\\\x=(15)/(3)\\\\x=5`