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.\newlineEmma likes to knit hats and mittens for friends and family. Last fall, she knitted 11 hat and 33 pairs of mittens, which took a total of 4646 hours. This fall, she knitted 11 hat and 11 pair of mittens, which took a total of 1818 hours. If each hat takes the same amount of time and each pair of mittens takes the same time, how long does it take Emma to knit each item?\newlineIt takes Emma _\_ hours to knit a hat and _\_ hours to knit a pair of mittens.

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.\newlineEmma likes to knit hats and mittens for friends and family. Last fall, she knitted 11 hat and 33 pairs of mittens, which took a total of 4646 hours. This fall, she knitted 11 hat and 11 pair of mittens, which took a total of 1818 hours. If each hat takes the same amount of time and each pair of mittens takes the same time, how long does it take Emma to knit each item?\newlineIt takes Emma _\_ hours to knit a hat and _\_ hours to knit a pair of mittens.
  1. Define Variables: Let's denote the time it takes Emma to knit a hat as hh hours and the time it takes to knit a pair of mittens as mm hours. From the first scenario, we have the equation h+3m=46h + 3m = 46 because she knitted 11 hat and 33 pairs of mittens in 4646 hours.
  2. Form Equations: From the second scenario, we have the equation h+m=18h + m = 18 because she knitted 11 hat and 11 pair of mittens in 1818 hours.
  3. Elimination Method: We now have a system of two equations. We will use elimination to solve for hh and mm. To eliminate hh, we can subtract the second equation from the first equation.
  4. Subtract Equations: Subtracting the second equation from the first, we get (h+3m)−(h+m)=46−18(h + 3m) - (h + m) = 46 - 18, which simplifies to 2m=282m = 28.
  5. Solve for m: Solving for m, we divide both sides of the equation by 22, giving us m=14m = 14. This means it takes Emma 1414 hours to knit a pair of mittens.
  6. Substitute into Equation: Now that we know mm, we can substitute it back into the second equation to find hh. Substituting m=14m = 14 into h+m=18h + m = 18 gives us h+14=18h + 14 = 18.
  7. Final Solution: Solving for hh, we subtract 1414 from both sides of the equation, giving us h=18−14h = 18 - 14, which simplifies to h=4h = 4. This means it takes Emma 44 hours to knit a hat.

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