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

Question

2 years ago

12

each banner?

2 answers:

goldenfox [79] · Answer 1 · 2023-07-03T12:07:59+03:00

7 0

Answer:

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

Step-by-step explanation:

denis-greek [22] · Answer 2 · 2023-07-03T13:34:42+03:00

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

Step-by-step 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:

$x=1.$