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 any method, and fill in the blanks.\newlineGavin works in the shipping department of a toy manufacturer. Toy cars weigh 11 kilogram apiece and are shipped in a container that weighs 77 kilograms when empty. Toy trucks, which weigh 22 kilograms apiece, are shipped in a container weighing 44 kilograms. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys? What is the weight of each container?\newlineThere are __\_\_ toys in each container, for a total weight of __\_\_ kilograms.

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 any method: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineGavin works in the shipping department of a toy manufacturer. Toy cars weigh 11 kilogram apiece and are shipped in a container that weighs 77 kilograms when empty. Toy trucks, which weigh 22 kilograms apiece, are shipped in a container weighing 44 kilograms. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys? What is the weight of each container?\newlineThere are __\_\_ toys in each container, for a total weight of __\_\_ kilograms.
  1. Define Variables: Let xx be the number of toy cars and yy be the number of toy trucks. Since both kinds of containers have the same number of toys, we have:\newlinex=yx = y
  2. Calculate Weight of Toy Cars Container: The weight of the container with toy cars is 11 kilogram per car plus the weight of the empty container, which is 77 kilograms. So, the total weight of the container with toy cars is:\newlineWeight of toy cars container = 1×x+71 \times x + 7
  3. Calculate Weight of Toy Trucks Container: The weight of the container with toy trucks is 22 kilograms per truck plus the weight of the empty container, which is 44 kilograms. So, the total weight of the container with toy trucks is:\newlineWeight of toy trucks container = 2×y+42 \times y + 4
  4. Set Weight Equations Equal: Since both containers have the same weight when packed with toys, we can set the weights equal to each other:\newline1×x+7=2×y+41 \times x + 7 = 2 \times y + 4
  5. Substitute Variables: Using the fact that x=yx = y, we can substitute yy for xx in the equation:\newline1×y+7=2×y+41 \times y + 7 = 2 \times y + 4
  6. Solve for y: Now we solve for y:\newline1y+7=2y+41y + 7 = 2y + 4\newline7−4=2y−1y7 - 4 = 2y - 1y\newline3=y3 = y
  7. Find Total Weight of Toy Cars Container: Since x=yx = y, we also have:\newlinex=3x = 3
  8. Find Total Weight of Toy Trucks Container: Now we can find the total weight of each container. For the toy cars container:\newlineWeight of toy cars container = 1×x+7=1×3+7=101 \times x + 7 = 1 \times 3 + 7 = 10 kilograms
  9. Find Total Weight of Toy Trucks Container: Now we can find the total weight of each container. For the toy cars container:\newlineWeight of toy cars container = 1×x+7=1×3+7=101 \times x + 7 = 1 \times 3 + 7 = 10 kilogramsFor the toy trucks container:\newlineWeight of toy trucks container = 2×y+4=2×3+4=102 \times y + 4 = 2 \times 3 + 4 = 10 kilograms

More problems from Solve a system of equations using any method: 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 (187)

Related topics

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