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

Answer:

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

Step-by-step 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

$y=\frac{x}{2}$

Now, we replace the second equation into the first one

$2x+3y=1421\\2x+3(\frac{x}{2})=1421\\\frac{4x+3x}{2}=1421\\\frac{7x}{2}=1421\\ x=\frac{2(1421)}{7}=406$

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

$y=\frac{x}{2}\\y=\frac{406}{2}=203$

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