Systems of equations word problems example 1 | Algebra I | Khan Academy

TL;DR

An electronics warehouse provides information about the weight of televisions and DVD players and how to solve a system of equations to find their individual weights.

Transcript

An electronics warehouse ships televisions and DVD players in certain combinations to retailers throughout the country. They tell us that the weight of 3 televisions and 5 DVD players is 62.5 pounds, and the weight of 3 televisions and 2 DVD players-- so they're giving us different combinations-- is 52 pounds. Create a system of equations that repr... Read More

Key Insights

• 🏋️ The electronic warehouse provided two statements involving the weights of televisions and DVD players, which can be translated into equations.
• 🪜 Solving the system of equations involves adding or subtracting equations to eliminate a variable.
• 🏋️ The weight of a DVD player is determined to be 3.5 pounds, while the weight of a television is 15 pounds.

Questions & Answers

Q: How can the information provided by the electronics warehouse be represented as equations?

We can use the variables t (weight of a television) and d (weight of a DVD player) to create the equations. One equation is 3t + 5d = 62.5, and the other is 3t + 2d = 52.

Q: What is the process for solving the system of equations?

One approach is to eliminate one variable by multiplying one equation by a factor and adding it to the other equation. In this case, we multiplied the second equation by -1 and added it to the first equation to cancel out the 3t terms.

Q: What is the weight of a DVD player?

After solving the system of equations, we find that the weight of a DVD player is 3.5 pounds.

Q: What is the weight of a television?

Substituting the weight of a DVD player into one of the equations, we find that the weight of a television is 15 pounds.

Summary & Key Takeaways

• An electronics warehouse states that the weight of 3 televisions and 5 DVD players is 62.5 pounds.

• The weight of 3 televisions and 2 DVD players is said to be 52 pounds.

• By creating and solving a system of equations, the weights of televisions and DVD players are determined to be 15 pounds and 3.5 pounds, respectively.