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 postal service offers flat-rate shipping for priority mail in special boxes. Today, Pam shipped 99 small boxes and 66 large boxes, which cost her $138\$138 to ship. Meanwhile, Donald shipped 33 small boxes and 77 large boxes, and paid $116\$116. How much does it cost to ship these two sizes of box?\newlineShipping costs $____\$\_\_\_\_ for a small box and $____\$\_\_\_\_ for a large box.

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 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 postal service offers flat-rate shipping for priority mail in special boxes. Today, Pam shipped 99 small boxes and 66 large boxes, which cost her $138\$138 to ship. Meanwhile, Donald shipped 33 small boxes and 77 large boxes, and paid $116\$116. How much does it cost to ship these two sizes of box?\newlineShipping costs $____\$\_\_\_\_ for a small box and $____\$\_\_\_\_ for a large box.
  1. Define variables: Define the variables for the cost of shipping a small box and a large box.\newlineLet xx be the cost to ship a small box, and yy be the cost to ship a large box.
  2. Write Pam's equation: Write the equation for Pam's shipment.\newlinePam shipped 99 small boxes and 66 large boxes for $138\$138.\newlineThe equation is: 9x+6y=1389x + 6y = 138.
  3. Write Donald's equation: Write the equation for Donald's shipment.\newlineDonald shipped 33 small boxes and 77 large boxes for $116\$116.\newlineThe equation is: 3x+7y=1163x + 7y = 116.
  4. Eliminate variable xx: Choose which variable to eliminate.\newlineWe will eliminate xx by multiplying the second equation by 33 to match the coefficient of xx in the first equation.
  5. Multiply second equation: Multiply the second equation by 33. \newline3(3x+7y)=3(116)3(3x + 7y) = 3(116)\newline9x+21y=3489x + 21y = 348
  6. Subtract equations: Subtract the first equation from the modified second equation to eliminate xx.$9x+21y\$9x + 21y - 9x+6y9x + 6y = 348348 - 138138\)9x+21y−9x−6y=348−1389x + 21y - 9x - 6y = 348 - 13815y=21015y = 210
  7. Solve for y: Solve for y.\newline15y=21015y = 210\newliney=21015y = \frac{210}{15}\newliney=14y = 14
  8. Substitute y value: Substitute the value of y into one of the original equations to solve for x.\newlineUsing the first equation: 9x+6(14)=1389x + 6(14) = 138\newline9x+84=1389x + 84 = 138\newline9x=138−849x = 138 - 84\newline9x=549x = 54
  9. Solve for x: Solve for x.\newline9x=549x = 54\newlinex=549x = \frac{54}{9}\newlinex=6x = 6

More problems from Solve a system of equations using elimination: 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 (61)

Related topics

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