Question

The cost of 2 televisions and 3 dvd players is $1421. The cost of 1 dvd is half the cost of 1 television.what is the cost of 1 television?

Answer 1

The total cost of one television is $406. There is an explanation in the picture.

Answer 2

The cost of one tv is $406, and the cost of one dvd is $203.

Explanation:

We know that

2 tv's and 3 dvd's cost $1421

Let's call
`x` tv's and
`y` dvd's. So, this statement can be modelled as

`2x+3y=1421`

The cost of 1 dvd is half of the cost of 1 tv. This can be expressed

`y=(x)/(2)`

Now, we replace the second equation into the first one

`2x+3y=1421\\2x+3((x)/(2))=1421\\(4x+3x)/(2)=1421\\(7x)/(2)=1421\\ x=(2(1421))/(7)=406`

Then, we replace this value in one equation to find the other value

`y=(x)/(2)\\y=(406)/(2)=203`

Therefore, the cost of one tv is $406, and the cost of one dvd is $203.