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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Sparkles the Clown makes balloon animals for children at birthday parties. At Aubrey's party, he made $4$ balloon poodles and $4$ balloon giraffes, which used a total of $20$ balloons. For Josie's party, he used $13$ balloons to make $5$ balloon poodles and $1$ balloon giraffe. How many balloons does each animal require? $\newline$ Each poodle requires _ balloons and each giraffe requires _ balloons.

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Solve a system of equations using any method: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Sparkles the Clown makes balloon animals for children at birthday parties. At Aubrey's party, he made

4

balloon poodles and

4

balloon giraffes, which used a total of

20

balloons. For Josie's party, he used

13

balloons to make

5

balloon poodles and

1

balloon giraffe. How many balloons does each animal require?

\newline

Each poodle requires _____ balloons and each giraffe requires _____ balloons.

Define Variables: Let's define variables for the number of balloons required for each animal. $\newline$ Let $p$ be the number of balloons required for a poodle. $\newline$ Let $g$ be the number of balloons required for a giraffe.
Write Equations: Write the system of equations based on the given information. $\newline$ For Aubrey's party: $4p + 4g = 20$ $\newline$ For Josie's party: $5p + 1g = 13$
Elimination Method: Solve the system of equations using any method. We will use the substitution or elimination method. Let's use the elimination method by multiplying the second equation by $4$ to match the coefficient of $g$ in the first equation. $\newline$ $4(5p + 1g) = 4(13)$ $\newline$ $20p + 4g = 52$
Subtract Equations: Now we have two equations with the same coefficient for $g$ : $4p + 4g = 20$ $20p + 4g = 52$ Subtract the first equation from the second to eliminate $g$ . $(20p + 4g) - (4p + 4g) = 52 - 20$ $20p - 4p = 32$ $16p = 32$
Solve for p: Solve for p. $\newline$ $16p = 32$ $\newline$ $p = \frac{32}{16}$ $\newline$ $p = 2$
Substitute for g: Substitute the value of $p$ into one of the original equations to solve for $g$ . Using the second equation: $5p + 1g = 13$ $5(2) + g = 13$ $10 + g = 13$ $g = 13 - 10$ $g = 3$
Final Balloon Count: We found: $\newline$ p = $2$ $\newline$ g = $3$ $\newline$ Each poodle requires $2$ balloons and each giraffe requires $3$ balloons.

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