math questions please help

Question

The monthly cost C, in dollars, for calls from the United States to Japan on a certain phone plan is modeled by the function 𝐶(𝑥) = 0.07𝑥 + 24.99 Where x is the number of minutes used and C is in dollars a) What is the cost if you talk on the phone for 45 minutes? b) Suppose that your monthly bill is $40, how many minutes did you use on the phone? c) Suppose that your monthly budget only allows $50 on the phone. What is the maximum number of minutes that you can talk? d) Suppose 𝐷(𝑥) models another phone plan that charges 𝐷(𝑥) = 0.14𝑥 + 10.99 Where x is the number of minutes used and C is in dollars If you typically can only spend $50 a month for the phone, which plan 𝐶(𝑥) or 𝐷(𝑥) would provide more minutes per month?

Answer 1

C =.07x +24.99

if x = 45

C = .07(45) + 24.99 = 3.15+24.99= $28.14 for 45 minutes

if your bill is $40

40=.07x +24.99

.07x = 40-24.99 = 15.01

x = 15.01/.07 = 1501/7 = 214 3/7 minutes

For $50

50=.07x +24.99

.07x = 50-24.99= 25.01

x= 25.01/.07 = 2501/7 = 357 2/7 minutes

D(x) =.14x +10.99 = C(x) =.07x +24.99

.07x = 24.99-10.99 = 14

x = 14/.07 = 1400/7 = 200 minutes when the cost is the same for either plan

for less than 200 minutes plan D(x) is less expensive

for more than 200 minutes plan C(x) is less expensive

for 200 minutes, both plans cost the same .14(200)+10.99 = $38.99 = .07(200)+24.99