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.\newlineA TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 66 sitcoms and 55 dramas, for a total of 416416 minutes of programming, not counting commercials. On Tuesday nights, he has scheduled 55 sitcoms and 55 dramas, for a total of 390390 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?\newlineSitcoms are _\_ minutes long and dramas are _\_ minutes long.

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.\newlineA TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 66 sitcoms and 55 dramas, for a total of 416416 minutes of programming, not counting commercials. On Tuesday nights, he has scheduled 55 sitcoms and 55 dramas, for a total of 390390 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?\newlineSitcoms are _\_ minutes long and dramas are _\_ minutes long.
  1. Denote Lengths: Let's denote the length of a sitcom as 'ss' minutes and the length of a drama as 'dd' minutes.\newlineWe need to set up two equations based on the given information.
  2. Equation for Monday: For Monday nights, the total time for 66 sitcoms and 55 dramas is 416416 minutes. This gives us the equation:\newline6s+5d=4166s + 5d = 416
  3. Equation for Tuesday: For Tuesday nights, the total time for 55 sitcoms and 55 dramas is 390390 minutes. This gives us the equation:\newline5s+5d=3905s + 5d = 390
  4. System of Equations: We now have a system of two equations:\newline6s+5d=4166s + 5d = 416\newline5s+5d=3905s + 5d = 390\newlineWe can solve this system using the method of elimination or substitution. Let's use elimination.
  5. Elimination Method: To eliminate one of the variables, we can subtract the second equation from the first equation: \newline(6s+5d)−(5s+5d)=416−390(6s + 5d) - (5s + 5d) = 416 - 390\newline6s−5s+5d−5d=266s - 5s + 5d - 5d = 26\newlines=26s = 26
  6. Find 's' Value: Now that we have the value of 's', we can substitute it back into one of the original equations to find 'd'. Let's use the second equation:\newline5s+5d=3905s + 5d = 390\newline5(26)+5d=3905(26) + 5d = 390\newline130+5d=390130 + 5d = 390
  7. Substitute to Find 'd': Subtract 130130 from both sides of the equation to solve for 'd':\newline130+5d−130=390−130130 + 5d - 130 = 390 - 130\newline5d=2605d = 260\newlined=2605d = \frac{260}{5}\newlined=52d = 52

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