Each month, Allen pays a total of $150 for both cable TV and internet service. If he were to switch to a rival service provider, he would pay $70 less per month for cable TV service and twice as much per month for internet service. To save $20 per month total, how much would Allen have to pay for cable TV service per month to the rival provider?
If he pays s for internet service and c for cable, then
s+c = 150
we want c such that
(c-70)+2s = 150-20
c-70+2(150-c) = 130
c = 100
check:
cable costs 100
internet costs 50
on the new plan,
cable costs 30
internet costs 100
for a total of 130 = 150-20
Well, it seems like Allen is in for some tricky negotiations! Let's break it down:
Currently, Allen pays a total of $150 for cable TV and internet service.
If he were to switch to a rival provider, he would pay $70 less per month for cable TV service. That means he would pay $150 - $70 = $80 per month for cable TV.
He would also pay twice as much per month for internet service. So, if he currently pays x amount for internet, he would pay 2x for the new provider.
To save $20 per month in total, Allen would have to pay $150 - $20 = $130 per month for both services with the rival provider.
Now, let's add up the costs for the new provider:
$80 for cable TV + 2x for internet = $130 in total.
So, Allen would have to pay $80 per month for cable TV service to the rival provider.
Remember, it's not just about the money, but also about finding a provider that makes you smile!
Let's assume Allen pays x dollars for cable TV service per month to the rival provider.
If he switches to the rival service provider, he would pay $70 less for cable TV service, which means he would pay (x - $70) dollars per month for cable TV.
He would also pay twice as much for internet service, so he would pay 2 * (x - $70) dollars per month for internet service.
To save $20 per month total, Allen would have to pay a total of 150 - $20 = $130 per month for both services with the rival provider.
Therefore, the equation is:
(x - $70) + 2 * (x - $70) = $130
Simplifying the equation:
3x - 140 = $130
Adding 140 to both sides:
3x = $270
Dividing both sides by 3:
x = $90
Therefore, Allen would have to pay $90 per month for cable TV service to the rival provider.
Let's break down the problem step by step.
Currently, Allen pays a total of $150 per month for both cable TV and internet service.
If he were to switch to a rival service provider, he would save $70 per month for cable TV service and pay twice as much per month for internet service.
To save a total of $20 per month, we need to find out how much Allen would have to pay for cable TV service per month to the rival provider.
Let's assume the cost of cable TV service with the rival provider is "x" dollars per month.
According to the given information, Allen would save $70 per month for cable TV service, so his new expense for cable TV would be $70 less than what he currently pays. Therefore, the cost of cable TV service with the rival provider would be (150 - 70) = $80 per month.
Now, let's find out how much Allen would have to pay for internet service with the rival provider.
Since he pays twice as much for internet service with the rival provider, his new expense for internet service would be (x * 2) dollars per month.
To save a total of $20 per month, Allen's new total expense with the rival provider would be the sum of his new expenses for cable TV and internet service.
So, (80 + (x * 2)) should equal $20 less than what he currently pays, which is $150.
Hence, we can set up the equation:
80 + (x * 2) = 150 - 20
Next, let's solve the equation to find the value of "x".
Subtracting 80 from both sides of the equation:
(x * 2) = 150 - 20 - 80
(x * 2) = 50
Dividing both sides of the equation by 2:
x = 25
Therefore, Allen would have to pay $25 per month for cable TV service to the rival provider in order to save $20 per month total.