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 an augmented matrix, and fill in the blanks.\newlineAndy loves riding Ferris wheels and roller coasters. While visiting the Morgan County Fair, he first went on the Ferris wheel 11 time, using a total of 22 tickets. Then, after taking a break and having a snack, Andy went on the Ferris wheel 22 times and the roller coaster 44 times, using a total of 2020 tickets. How many tickets does it take to ride each attraction?\newlineIt takes ____\_\_\_\_ tickets to ride the Ferris wheel, and ____\_\_\_\_ tickets to ride the roller coaster.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of equations using elimination: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAndy loves riding Ferris wheels and roller coasters. While visiting the Morgan County Fair, he first went on the Ferris wheel 11 time, using a total of 22 tickets. Then, after taking a break and having a snack, Andy went on the Ferris wheel 22 times and the roller coaster 44 times, using a total of 2020 tickets. How many tickets does it take to ride each attraction?\newlineIt takes ____\_\_\_\_ tickets to ride the Ferris wheel, and ____\_\_\_\_ tickets to ride the roller coaster.
  1. Define Variables: Let xx be the number of tickets for the Ferris wheel and yy be the number of tickets for the roller coaster. Andy's first ride gives the equation 1x+0y=21x + 0y = 2.
  2. Form Equations: Andy's second set of rides gives the equation 2x+4y=202x + 4y = 20.
  3. Create Augmented Matrix: Write the system of equations as an augmented matrix: [1amp;0amp;2 2amp;4amp;20]\left[\begin{array}{ccc} 1 & 0 & 2 \ 2 & 4 & 20 \end{array}\right].
  4. Eliminate Variable xx: Multiply the first row by −2-2 and add it to the second row to eliminate xx from the second equation: new second row is [0,4,16][0, 4, 16].
  5. Solve for y: Divide the second row by 44 to solve for yy: y=4y = 4.
  6. Solve for xx: Substitute y=4y = 4 into the first equation to solve for xx: 1x+0(4)=21x + 0(4) = 2, so x=2x = 2.
  7. Check Solution: Check the solution by substituting xx and yy into the second equation: 2(2)+4(4)=4+16=202(2) + 4(4) = 4 + 16 = 20, which is correct.

More problems from Solve a system of equations using elimination: word problems

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (1,1)(1,1) a solution to this system of equations? \newline4x+10y=144x + 10y = 14\newlinex+6y=7x + 6y = 7\newlineChoices:\newline(A) yes \newline(B) no
Get tutor helpright-arrow

Posted 5 months ago

Question
Which describes the system of equations below?\newliney=–3x+9y = –3x + 9 \newliney=–3x+9y = –3x + 9 \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 elimination. \newline7x−8y=−17 7x - 8y = -17 \newline −7x+3y=2 -7x + 3y = 2 \newline (____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 9 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve the system of equations by substitution.\newline−3x−y−3z=−11-3x - y - 3z = -11\newlinez=5z = 5\newlinex−y+3z=19x - y + 3z = 19\newline(____.____,____)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations by elimination.\newlinex−3y−2z=10 x - 3y - 2z = 10 \newline3x+2y+2z=14 3x + 2y + 2z = 14 \newline2x−3y−2z=16 2x - 3y - 2z = 16 \newline(_,_,_)(\_,\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x−37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=−x−24 y = -x - 24 \newlinex2+y2=488 x^2 + y^2 = 488 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

View all (43)

Related topics

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