Understanding Linear Equations in a Factory Setting

The video tutorial presents a problem involving a toy factory with machines and workers. Each machine produces 14 toys, and each worker packs 2 toys, leaving 40 toys unpacked. The number of workers is eight less than seven times the number of machines. The tutorial defines variables for machines and workers, sets up equations, and attempts to solve them. However, the solution reveals that the equations are inconsistent, leading to the conclusion that no solution exists for the given constraints.

What is the main task of the factory's machines?

• To sell toys

• To transport toys

• To produce toys

• To pack toys

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CCSS.6.EE.B.6

How many toys does each machine produce in a day?

• 10 toys

• 14 toys

• 16 toys

• 12 toys

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CCSS.6.EE.B.6

What variable is used to represent the number of machines?

• W

• N

• M

• T

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CCSS.6.EE.B.7

How many toys does each worker pack?

• Three toys

• Two toys

• Four toys

• One toy

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CCSS.6.EE.C.9

What is the relationship between the number of workers and machines?

• Workers are twice the number of machines

• Workers are equal to the number of machines

• Workers are eight less than seven times the number of machines

• Workers are seven more than eight times the number of machines

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CCSS.6.EE.B.6

What is the equation for the number of toys produced?

• 2M

• 14M

• 2W

• 14W

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What method is used to solve the equations?

• Graphical method

• Trial and error

• Substitution method

• Elimination method

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CCSS.8.EE.C.8B

What is the result of the substitution in the equations?

• No solution

• An infinite number of solutions

• A valid solution

• A single solution

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CCSS.8.EE.C.8B

Why is there no solution to the problem?

• The problem is not solvable

• The equations are too complex

• The equations are inconsistent

• The variables are not defined

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CCSS.RI.6.2

CCSS.RI.7.2

CCSS.RL.6.2

CCSS.RL.7.2

CCSS.RL.8.2

What does the conclusion of the problem highlight?

• The role of workers in production

• The importance of checking solutions

• The need for more machines

• The efficiency of the factory

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CCSS.RI.6.2

CCSS.RI.7.2

CCSS.RL.6.2

CCSS.RL.7.2

CCSS.RL.8.2