jasper wants to join a video store, blockbuster offers $9.99 for one year. with the discount card, each video rental costs $2.49. a discount card frm video time costs $20.49 for 1 year. with the video time discount card, each vido rental costs $1.79.
a) after hw many video rentals is the membership costs the same?
b) what is the cost when they are equal
To find out after how many video rentals the membership costs would be the same, we need to compare the total costs of the two options and look for the point where they intersect.
Let's start by calculating the total cost with the Blockbuster membership:
Total cost with Blockbuster = Membership cost + (Number of rentals * Cost per rental)
The membership cost for Blockbuster is $9.99 for one year, and the cost per rental is $2.49.
So the total cost with Blockbuster would be:
Total cost with Blockbuster = $9.99 + (Number of rentals * $2.49)
Next, let's calculate the total cost with the Video Time discount card:
Total cost with Video Time = Membership cost + (Number of rentals * Cost per rental)
The membership cost for Video Time is $20.49 for one year, and the cost per rental is $1.79.
So the total cost with Video Time would be:
Total cost with Video Time = $20.49 + (Number of rentals * $1.79)
To find the point where the costs are the same, we need to set these two total cost equations equal to each other and solve for the number of rentals:
$9.99 + (Number of rentals * $2.49) = $20.49 + (Number of rentals * $1.79)
Now, let's solve this equation:
$9.99 + $2.49 * Number of rentals = $20.49 + $1.79 * Number of rentals
To isolate the number of rentals, let's subtract $1.79 * Number of rentals from both sides:
$9.99 + $2.49 * Number of rentals - $1.79 * Number of rentals = $20.49
Simplifying the equation:
$9.99 + $0.70 * Number of rentals = $20.49
Now, let's isolate the Number of rentals by subtracting $9.99 from both sides:
$0.70 * Number of rentals = $20.49 - $9.99
Simplifying further:
$0.70 * Number of rentals = $10.50
To find the value of Number of rentals, we need to divide both sides by $0.70:
Number of rentals = $10.50 / $0.70 = 15
So, after 15 video rentals, the membership costs for Blockbuster and Video Time would be the same.
Now, let's calculate the cost when they are equal:
For 15 rentals, let's calculate the total cost with both options:
Total cost with Blockbuster = $9.99 + (15 * $2.49) = $44.34
Total cost with Video Time = $20.49 + (15 * $1.79) = $48.24
Therefore, the cost when they are equal is approximately $44.34