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 substitution, and fill in the blanks.\newlineTwo sisters have decided to watch all the episodes of a popular TV show on DVD. Sophia has already watched 33 episodes and will continue to watch the show at a rate of 11 episode per day. Jenny, who hasn't yet seen the show, will start watching 44 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?\newlineIn _\_ days, the sisters will each have watched _\_ episodes of the show.

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 substitution: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineTwo sisters have decided to watch all the episodes of a popular TV show on DVD. Sophia has already watched 33 episodes and will continue to watch the show at a rate of 11 episode per day. Jenny, who hasn't yet seen the show, will start watching 44 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?\newlineIn _\_ days, the sisters will each have watched _\_ episodes of the show.
  1. Define Variables: Let xx represent the number of days and yy represent the number of episodes watched.\newlineFor Sophia:\newlineNumber of episodes already watched: 33\newlineWatching rate of episodes per day: 11\newlineThe equation based on the given information is:\newlineEpisodes watched = watching rate ×\times days + number of episodes already watched\newliney=1x+3y = 1x + 3\newlineFor Sophia, the equation is: y=x+3y = x + 3
  2. Sophia's Equation: For Jenny:\newlineNumber of episodes already watched: 00 (since she hasn't started yet)\newlineWatching rate of episodes per day: 44\newlineThe equation based on the given information is:\newlineEpisodes watched = watching rate ×\times days + number of episodes already watched\newliney=4x+0y = 4x + 0\newlineFor Jenny, the equation is: y=4xy = 4x
  3. Jenny's Equation: System of equations:\newliney=x+3y = x + 3\newliney=4xy = 4x\newlineTo find the point where they have watched the same number of episodes, set the two equations equal to each other.\newlinex+3=4xx + 3 = 4x
  4. System of Equations: Solve for xx by isolating the variable.\newlineSubtract xx from both sides of the equation:\newlinex+3−x=4x−xx + 3 - x = 4x - x\newline3=3x3 = 3x\newlineNow, divide both sides by 33 to solve for xx:\newline33=3x3\frac{3}{3} = \frac{3x}{3}\newline1=x1 = x\newlineSo, x=1x = 1
  5. Solve for xx: Find the value of yy by substituting xx into one of the original equations.\newlineSubstitute 11 for xx in y=4xy = 4x (Jenny's equation):\newliney=4(1)y = 4(1)\newliney=4y = 4\newlineSo, y=4y = 4
  6. Find yy: Verify the solution by substituting x=1x = 1 into Sophia's equation to ensure it gives the same yy value.\newlineSubstitute 11 for xx in y=x+3y = x + 3 (Sophia's equation):\newliney=1+3y = 1 + 3\newliney=4y = 4\newlineSince this matches the yy value found using Jenny's equation, the solution is correct.

More problems from Solve a system of equations using substitution: 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 (39)

Related topics

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