Question

7. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal

Answer 1

After 49 months the total cost of the two systems will be equal.

Explanation:

To Find: We need to find the number of months will the total cost of the two systems be equal

Solution:

For Satellite receiver:

Satellite receiver cost = $298.90

Monthly charge = $68.70

Let the Number of months be denoted by 'x'.

Now we can say that;

Total cost using Satellite receiver is equal to sum of Satellite receiver cost and Monthly charge multiplied by number of months.

framing in equation form we get;

Total cost using Satellite receiver =
`298.90+68.70x`

For Using Cable:

Monthly charge = $74.80

So we can say that;

Total cost using cable is equal to Monthly charge multiplied by number of months.

framing in equation form we get;

Total cost using cable =
`74.80x`

Now to find the number of months when both the cost will be the same so we will make both the equation equal we get;

`298.90+68.70x=74.80x`

Combining the like terms we get;

`74.80x-68.70x=298.90\\\\6.1x=298.90`

Dividing both side by 6.1 we get;

`(6.1x)/(6.1)=(298.90)/(6.1)\\\\x=49`

Hence After 49 months the total cost of the two systems will be equal.