MHB How much do 3 televisions cost?

[Johnx1]

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?

 

[joypav]

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.

 

[HOI]

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.

 

[Johnx1]

I'll keep in mind to write it in single variables. Thank you to everyone for showing a clear way to do it.