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

Answer:

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

Step-by-step 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;

$\frac{6.1x}{6.1}=\frac{298.90}{6.1}\\\\x=49$

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