Question

You buy 3 balloons and 2 banners for $7. Your friend buys 6 balloons and 3 banners for $12. What is the cost of each balloon? of each banner?

Answer 1

Answer: the cost of each balloon is $1, the cost of each banner is $2.

Explanation:

Let the cost of each balloon is x, and the cost of each banner is y.

Hence,

`\displaystyle\\\left \{ {{3x+2y=7\ \ \ \ (1)} \atop {6x+3y=12\ \ \ \ (2)}} \right. \\`

We multiply equation (1) by -2:

`\displaystyle\\\left \{ {{-6x-4y=-14} \atop {6x+3y=12}} \right. \\`

Let's sum up these equations:

`-y=-2\\`

Multiply both sides of the equation by -1:

`y=2.\\`

We substitute the value of y into equation (1):

`3x+2*2=7\\3x+4=7\\3x+4-4=7-4\\3x=3\\`

Divide both sides of the equation by 3:

`x=1.`

Answer 2

each balloon costs- $1; each banner costs- $2

Explanation: