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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Sparkles the Clown makes balloon animals for children at birthday parties. At Bridget's party, she made 2 balloon poodles and 4 balloon giraffes, which used a total of 22 balloons. For Erik's party, she used 15 balloons to make 1 balloon poodle and 3 balloon giraffes. How many balloons does each animal require? Each poodle requires balloons and each giraffe requires balloons

Answer :

Answer:

Each poodle requires 3 balloons and each giraffe requires 4 balloons.

Explanation:

Let's call x the number of balloons that each poodle requires and y the number of balloons that each giraffe requires.

If at Bridget's party, she used 22 balloons for 2 poodles and 4 giraffes, then we can write the following equation:

2x + 4y = 22

And if at Erik's party, she used 15 balloons for 1 poodle and 3 giraffes, we can write the second equation:

x + 3y = 15

Then, the system of equation is:

2x + 4y = 22

x + 3y = 15

Now, we can solve the second equation for x:

x + 3y = 15

x + 3y - 3y = 15 - 3y

x = 15 - 3y

Then, substitute x = 15 - 3y on the first equation and solve for y as:

2x + 4y = 22

2(15 - 3y) + 4y = 22

2(15) - 2(3y) + 4y = 22

30 - 6y + 4y = 22

30 - 2y = 22

30 - 2y - 30 = 22 - 30

-2y = -8

-2y/(-2) = -8/(-2)

y = 4

Finally, the value of x is equal to:

x = 15 - 3y

x = 15 - 3(4)

x = 15 - 12

x = 3

Therefore, each poodle requires 3 balloons and each giraffe requires 4 balloons.

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