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.\newlineA realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 33 twin beds and 55 queen beds and used a total of 7575 pillows. At another house, she used 1212 pillows to spruce up 11 queen bed. How many decorative pillows did the realtor arrange on each bed?\newlineThe realtor used ___\_\_\_ pillows on every twin bed and ___\_\_\_ pillows on every queen bed.

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.\newlineA realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated 33 twin beds and 55 queen beds and used a total of 7575 pillows. At another house, she used 1212 pillows to spruce up 11 queen bed. How many decorative pillows did the realtor arrange on each bed?\newlineThe realtor used ___\_\_\_ pillows on every twin bed and ___\_\_\_ pillows on every queen bed.
  1. First equation formulation: First equation based on 33 twin beds and 55 queen beds using 7575 pillows: 3t+5q=753t + 5q = 75.
  2. Second equation formulation: Second equation based on 11 queen bed using 1212 pillows: 0t+1q=120t + 1q = 12.
  3. Augmented matrix creation: Write the system of equations as an augmented matrix: ∣3amp;5amp;75 0amp;1amp;12∣\left| \begin{array}{cc|c} 3 & 5 & 75 \ 0 & 1 & 12 \end{array} \right|
  4. Matrix row operations: Use row operations to solve the matrix. Since the second row is already solved for qq (0t+1q=120t + 1q = 12), we can use it to find the value of qq.
  5. Substitute and solve for qq: q=12q = 12. Substitute qq into the first equation: 3t+5(12)=753t + 5(12) = 75.
  6. Calculate twin bed pillows: Calculate the number of pillows on each twin bed: 3t+60=753t + 60 = 75.
  7. Solve for tt: Subtract 6060 from both sides: 3t=153t = 15.
  8. Final solution: Divide by 33 to find tt: t=153t = \frac{15}{3}.
  9. Final solution: Divide by 33 to find tt: t=153t = \frac{15}{3}. t=5t = 5. So, the realtor uses 55 pillows on every twin bed and 1212 pillows on every queen bed.

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