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 elimination, and fill in the blanks.\newlineThe members of a sewing circle are making blankets to give to shelters. This week, they made 1414 twin-size blankets and 2727 queen-size blankets, using a total of 284284 yards of fabric. Last week, the members completed 4747 twin-size blankets and 4545 queen-size blankets, which required 497497 total yards of fabric. How much fabric is used for the different sizes of blankets?\newlineA twin-size blanket uses _\_ yards of fabric and a queen-size one uses _\_ yards.

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 elimination, and fill in the blanks.\newlineThe members of a sewing circle are making blankets to give to shelters. This week, they made 1414 twin-size blankets and 2727 queen-size blankets, using a total of 284284 yards of fabric. Last week, the members completed 4747 twin-size blankets and 4545 queen-size blankets, which required 497497 total yards of fabric. How much fabric is used for the different sizes of blankets?\newlineA twin-size blanket uses _\_ yards of fabric and a queen-size one uses _\_ yards.
  1. Define variables: Define variables for the fabric used per blanket type. Let tt be the yards of fabric per twin-size blanket and qq be the yards of fabric per queen-size blanket. From the problem, we have the equations:\newline- 14t+27q=28414t + 27q = 284 (this week's fabric usage)\newline- 47t+45q=49747t + 45q = 497 (last week's fabric usage)
  2. Use elimination: Use elimination to solve the system. Multiply the first equation by 4545 (the coefficient of qq in the second equation) and the second equation by 2727 (the coefficient of qq in the first equation):\newline- 630t+1215q=12780630t + 1215q = 12780\newline- 1269t+1215q=134191269t + 1215q = 13419
  3. Subtract equations: Subtract the first new equation from the second new equation to eliminate qq:−1269t+1215q−(630t+1215q)=13419−12780- 1269t + 1215q - (630t + 1215q) = 13419 - 12780−639t=639- 639t = 639
  4. Solve for t: Solve for t:\newline- t=639639t = \frac{639}{639}\newline- t=1t = 1
  5. Substitute t: Substitute t=1t = 1 back into the first original equation to solve for qq:\newline- 14(1)+27q=28414(1) + 27q = 284\newline- 14+27q=28414 + 27q = 284\newline- 27q=27027q = 270\newline- q=270/27q = 270 / 27\newline- q=10q = 10

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