Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineSparkles the Clown makes balloon animals for children at birthday parties. At Aubrey's party, he made 44 balloon poodles and 44 balloon giraffes, which used a total of 2020 balloons. For Josie's party, he used 1313 balloons to make 55 balloon poodles and 11 balloon giraffe. How many balloons does each animal require?\newlineEach poodle requires _____ balloons and each giraffe requires _____ balloons.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve a system of equations using any method: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineSparkles the Clown makes balloon animals for children at birthday parties. At Aubrey's party, he made 44 balloon poodles and 44 balloon giraffes, which used a total of 2020 balloons. For Josie's party, he used 1313 balloons to make 55 balloon poodles and 11 balloon giraffe. How many balloons does each animal require?\newlineEach poodle requires _____ balloons and each giraffe requires _____ balloons.
  1. Define Variables: Let's define variables for the number of balloons required for each animal.\newlineLet pp be the number of balloons required for a poodle.\newlineLet gg be the number of balloons required for a giraffe.
  2. Write Equations: Write the system of equations based on the given information.\newlineFor Aubrey's party: 4p+4g=204p + 4g = 20\newlineFor Josie's party: 5p+1g=135p + 1g = 13
  3. 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 44 to match the coefficient of gg in the first equation.\newline4(5p+1g)=4(13)4(5p + 1g) = 4(13)\newline20p+4g=5220p + 4g = 52
  4. Subtract Equations: Now we have two equations with the same coefficient for gg:4p+4g=204p + 4g = 2020p+4g=5220p + 4g = 52Subtract the first equation from the second to eliminate gg.(20p+4g)−(4p+4g)=52−20(20p + 4g) - (4p + 4g) = 52 - 2020p−4p=3220p - 4p = 3216p=3216p = 32
  5. Solve for p: Solve for p.\newline16p=3216p = 32\newlinep=3216p = \frac{32}{16}\newlinep=2p = 2
  6. Substitute for g: Substitute the value of pp into one of the original equations to solve for gg. Using the second equation: 5p+1g=135p + 1g = 13 5(2)+g=135(2) + g = 13 10+g=1310 + g = 13 g=13−10g = 13 - 10 g=3g = 3
  7. Final Balloon Count: We found:\newlinep = 22\newlineg = 33\newlineEach poodle requires 22 balloons and each giraffe requires 33 balloons.

More problems from Solve a system of equations using any method: word problems

Question
Solve using elimination.\newlinex+6y=−15x + 6y = -15\newline−2x+6y=12-2x + 6y = 12\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (1,1)(1,1) a solution to this system of equations?\newline8x+y=98x + y = 9\newline6x+12y=186x + 12y = 18\newlineChoices:\newline[[yes]\newline[no]]
Get tutor helpright-arrow

Posted 5 months ago

Question
How many solutions does the system of equations below have?\newliney = x − 77\newliney = x − 77\newlineChoices:\newline[A]no solution\text{[A]no solution}\newline[B]one solution\text{[B]one solution}\newline[C]infinitely many solutions\text{[C]infinitely many solutions}
Get tutor helpright-arrow

Posted 7 months ago

Question
Which describes the system of equations below?\newliney=17x−10y = \frac{1}{7}x - 10\newliney=17x−10y = \frac{1}{7}x - 10\newlineChoices:\newline[A]consistent and independent\text{[A]consistent and independent}\newline[B]consistent and dependent\text{[B]consistent and dependent}\newline[C]inconsistent\text{[C]inconsistent}
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve using substitution.\newliney=−5y = -5\newline−4x+3y=17-4x + 3y = 17\newline(_____, _____)
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLast Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read 22 pages per minute, and he had already read 9898 pages. Jayla, who has a reading speed of 33 pages per minute, had read 4848 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?\newlineAfter ____\_\_\_\_ minutes, Bryan and Jayla had each read ____\_\_\_\_ pages.
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAt the Castroville Ice Cream Parlor, one group of friends ordered 11 small serving of ice cream and 33 large servings of ice cream for 2020. Another group of friends ordered 11 small serving of ice cream and 44 large servings of ice cream for 2626. How much does the ice cream cost?\newlineThe ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve.\newliney=−1y = -1\newline−2x−4y=8-2x - 4y = 8\newline(_____ , _____)
Get tutor helpright-arrow

Posted 7 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineThere are two mystery numbers. The sum of 33 times the first number and 33 times the second number is −18-18. The sum of 22 times the first number and 33 times the second number is −13-13. What are the two numbers?\newlineThe first number is ______ , and the second number is ______.
Get tutor helpright-arrow

Posted 7 months ago

Question
A teacher purchased 300300 colored pencils for an upcoming project. The pencils she ordered come in packs of 2020 and packs of 3030. She ordered 1414 packs in all. Write a system of equations to find the number of 2020-pencil packs (x)(x) and 3030-pencil packs (y)(y) the art teacher ordered.
Get tutor helpright-arrow

Posted 8 months ago

View all (187)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant