Final answer:
The cost of the DVD player is $243, and the cost of the television is $729, given their total cost of $972 and that the television costs three times more than the DVD player.
Step-by-step explanation:
The question requires us to find the cost of a television and a DVD player given that their total cost is $972 and that the cost of the television is three times the cost of the DVD player.
To solve this, let's name the cost of the DVD player as x. Therefore, the cost of the television is three times the cost of the DVD player, which can be represented as 3x.
According to the given information, the sum of the cost of both the television and the DVD player is $972, so we can write the equation:
3x + x = $972
Combining like terms, we get:
4x = $972
To find the value of x, we divide both sides of the equation by 4:
x = $972 / 4
x = $243
So, the cost of the DVD player is $243. Now, we will find the cost of the television by multiplying the cost of the DVD player by 3:
Cost of the television = 3x
= 3 * $243
= $729
Therefore, the cost of the television is $729 and the cost of the DVD player is $243.