Question

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?

Answer 1

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