How much do 3 televisions cost?

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Discussion Overview

The discussion revolves around solving a problem involving the costs of televisions and washing machines. Participants explore how to set up equations based on the given information about total costs and price differences, focusing on algebraic expressions and methods for solving systems of equations.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant presents the initial equation based on the total cost of televisions and washing machines but expresses uncertainty about the algebraic setup.
  • Another participant suggests renaming the costs as variables (x for television cost and y for washing machine cost) to clarify the equations.
  • A third participant introduces single-letter variables (W for washing machine cost and T for television cost) and proposes a second equation based on the price difference between the two appliances.
  • Participants discuss the need for a second equation to solve the system, emphasizing the importance of correctly substituting variables in the equations.

Areas of Agreement / Disagreement

Participants generally agree on the need to establish a system of equations to solve the problem, but there is no consensus on the best approach to set up and solve these equations. Different variable naming conventions and methods are suggested without resolving which is superior.

Contextual Notes

Participants express uncertainty about specific algebraic steps and the implications of variable substitutions, indicating that the discussion is still in the exploratory phase.

Who May Find This Useful

Students or individuals seeking assistance with algebraic problem-solving, particularly in setting up and solving systems of equations related to word problems.

Johnx1
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The total cost of 2 similar televisions and 5 similar washing machines is \$7215. Each washing machine costs \$216 less than a television. How much do 3 televisions cost?my answer:
2 television + 5 washing machines = 7215but I got stuck there. However I dd look at how to do it, but I'm not 100% sure why they subtracted 432 from 7215. Is there a better algebraic expression that I have on top?

Unless it's: 2 television + 5 washing machines + 432 = 7215?
 
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Hey!

So what you are supposed to be thinking about in this problem is the "unknowns". What is the question? "How much do 3 televisions cost?" We know how many of each we are buying but we do not know what they cost.

"my answer: 2 television + 5 washing machines = 7215"

You are going in the right direction, but what you want to say is,

(2 televisions)(the cost of a television) + (5 washing machines)(the cost of a washing machine) = 7215

It will be much easier to rename these costs as variables. Let,

x = the cost of a television
y = the cost of a washing machine

Now we have a better looking equation.

2x + 5y = 7215

Now, to solve a system of equations using elimination (or substitution) we are going to need another equation! What else does the problem tell you?

"Each washing machine costs $216 less than a television."

Let's rewrite this using our variables.

the cost of a television - the cost of a washing machine = 216

or

x - y = 216

Awesome! Now we have two equations! So our system of equations is...

2x + 5y = 7215
x - y = 216


Try solving the system using the method of elimination or substitution.
 
Let "W" be the cost of a single washing machine and let "T" be the cost of a single television set.

"The total cost of 2 similar televisions and 5 similar washing machines is 7215".
So 2T+ 5W= 7215.

That is what you have though I think it is simpler, and less error prone, to use single letters rather than full words (clearly stating what those letters represent). This is a single equation in two unknowns so we need another equation in order to solve for specific values of T and W.

"Each washing machine costs $216 less than a television." This is our second equation:
W= T- 216.

You want to solve 2T+ 5W= 7215 and W= T- 216. The obvious thing to do is to replace W in the first equation by T- 216: 2T+ 5(T- 216)= 7215.
 
I'll keep in mind to write it in single variables. Thank you to everyone for showing a clear way to do it.
 

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