Math (functions)

Question

Kahlil pays a monthly fee for his cell phone. His plan includes unlimited text, but he has to pay for each minute he talks on the phone. In one month, he spent 240 minutes on the phone, and paid $22.40. In another month, he spent 360 minutes on the phone, and paid $26.60.

Let x be the number of minutes he talks on the phone in a month, and let f(×) be the total bill.

A) Write an expression to represent f: f(×)=

B) If Kahlil spent 170 minutes on the phone in one month, how much would he pay?

C) If in a month he paid $29.05 of cell phone bill he must have spent how many minutes on the phone in that month?

Answer 1

2240 = f + 240m, $22.40 for 240 minutes

2660 = f + 360m, $26.60 for 360 minutes

subtract 1st from 2nd equation to eliminate f

420 = 120m

m = 120/420 =12/42 =2/7 cents per minute

f = 2240 -240(2/7) = 2240-68.57= 2171.43= $21.71 monthly fee

f(x) = 2171.43 + (2/7)x where x = number of minutes

170 = 2171.43 +170(2/7) = 2171.43 +340/7= 2171.43 +10.5469 = 2182 = $21.82

$29.05 means how many minutes

2905 = 2171.43 +2x/7

2x/7 = 2905-2171.43 = 733.57

x = 7(733.57)/2 = 2567 minutes