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.\newlineAllie is going to ship some gifts to family members, and she is considering two shipping companies. The first shipping company charges a fee of $16\$16 to ship a medium box, plus an additional $6\$6 per kilogram. A second shipping company charges $12\$12 for the same size of box, plus an additional $8\$8 per kilogram. At a certain weight, the two shipping methods will cost the same amount. How much will it cost? What is that weight?\newlineThe two shipping methods both cost $\$_____ at a weight of _____ kilograms.

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.\newlineAllie is going to ship some gifts to family members, and she is considering two shipping companies. The first shipping company charges a fee of $16\$16 to ship a medium box, plus an additional $6\$6 per kilogram. A second shipping company charges $12\$12 for the same size of box, plus an additional $8\$8 per kilogram. At a certain weight, the two shipping methods will cost the same amount. How much will it cost? What is that weight?\newlineThe two shipping methods both cost $\$_____ at a weight of _____ kilograms.
  1. Representation of Variables: Let xx represent the weight in kilograms and yy represent the total cost in dollars. \newlineFor the first shipping company: \newlineBase fee: $16\$16 \newlineCost per kilogram: $6\$6 \newlineEquation based on the given information: \newlineTotal cost = base fee + (cost per kilogram * weight) \newliney=6x+16y = 6x + 16 \newlineFor the first company, the equation is: y=6x+16y = 6x + 16
  2. First Shipping Company: For the second shipping company: \newlineBase fee: $12\$12 \newlineCost per kilogram: $8\$8 \newlineEquation based on the given information: \newlineTotal cost = base fee + (cost per kilogram ∗* weight) \newliney=8x+12y = 8x + 12 \newlineFor the second company, the equation is: y=8x+12y = 8x + 12
  3. Second Shipping Company: System of equations: \newliney=6x+16y = 6x + 16 \newliney=8x+12y = 8x + 12 \newlineTo find the weight at which the cost is the same, set the two equations equal to each other. \newline6x+16=8x+126x + 16 = 8x + 12
  4. System of Equations: Solve for xx: \newlineSubtract 6x6x from both sides of the equation: \newline6x+16−6x=8x+12−6x6x + 16 - 6x = 8x + 12 - 6x \newline16=2x+1216 = 2x + 12
  5. Solving for x: Subtract 1212 from both sides of the equation: \newline16−12=2x+12−1216 - 12 = 2x + 12 - 12 \newline4=2x4 = 2x
  6. Substituting xx into Equation: Divide both sides by 22 to solve for xx: \newline42=2x2\frac{4}{2} = \frac{2x}{2} \newline2=x2 = x \newlineSo, x=2x = 2
  7. Final Result: We found x=2x = 2. Now, find the value of yy by substituting xx into one of the original equations. \newlineSubstitute 22 for xx in y=6x+16y = 6x + 16: \newliney=6(2)+16y = 6(2) + 16 \newliney=12+16y = 12 + 16 \newliney=28y = 28 \newlineSo, y=28y = 28
  8. Final Result: We found x=2x = 2. Now, find the value of yy by substituting xx into one of the original equations. \newlineSubstitute 22 for xx in y=6x+16y = 6x + 16: \newliney=6(2)+16y = 6(2) + 16 \newliney=12+16y = 12 + 16 \newliney=28y = 28 \newlineSo, y=28y = 28 We found: \newlinex=2x = 2 \newliney=28y = 28 \newlineThe weight at which both shipping methods cost the same is 22 kilograms, and the cost at that weight is yy33.

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 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 (39)

Related topics

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