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.\newlineJulian and Lee went to an arcade where the machines took tokens. Julian played 44 games of skee ball and 33 games of pinball, using a total of 1717 tokens. At the same time, Lee played 11 game of pinball, using up 33 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires ____\_\_\_\_ tokens, and every game of pinball requires ____\_\_\_\_ tokens.

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 any method: 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.\newlineJulian and Lee went to an arcade where the machines took tokens. Julian played 44 games of skee ball and 33 games of pinball, using a total of 1717 tokens. At the same time, Lee played 11 game of pinball, using up 33 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires ____\_\_\_\_ tokens, and every game of pinball requires ____\_\_\_\_ tokens.
  1. Define Variables: Let xx be the number of tokens required for a game of skee ball and yy for a game of pinball. Julian's games give us the equation 4x+3y=174x + 3y = 17.
  2. Julian's Equation: Lee's single game of pinball gives us the equation y=3y = 3.
  3. System of Equations: We now have the system of equations: 4x+3y=174x + 3y = 17 y=3y = 3
  4. Augmented Matrix: To solve using an augmented matrix, we write the coefficients of the variables and the constants in a matrix: [4amp;3amp;∣amp;17 0amp;1amp;∣amp;3]\begin{bmatrix} 4 & 3 & | & 17 \ 0 & 1 & | & 3 \end{bmatrix}
  5. Eliminate Variable: Since the second equation is already solved for yy, we can use it to eliminate yy from the first equation. We'll multiply the second row by −3-3 and add it to the first row.
  6. Multiply and Add: Multiplying the second row by −3-3 gives us:\newline[0−3∣−9][0 -3 | -9]
  7. Updated Matrix: Adding this to the first row:\newline[40∣8][4 0 | 8]
  8. Solve for xx: Now we have the matrix: [4amp;0amp;∣amp;8 0amp;1amp;∣amp;3]\begin{bmatrix} 4 & 0 & \vert & 8 \ 0 & 1 & \vert & 3 \end{bmatrix}
  9. Solve for y: From the first row of the matrix, we have 4x=84x = 8, which gives us x=2x = 2.
  10. Final Token Requirements: We already know y=3y = 3 from the second row of the matrix.
  11. Final Token Requirements: We already know y=3y = 3 from the second row of the matrix.So, every game of skee ball requires 22 tokens, and every game of pinball requires 33 tokens.

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

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

Posted 6 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 6 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 6 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 6 months ago

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

Posted 10 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 10 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 6 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 6 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 6 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 6 months ago

View all (92)

Related topics

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