The monthly cost of a wireless telephone plan is $39.99 for up to 450 min of calling time plus $0.45 per minute for each minute over 450 min.

Question

The monthly cost of a wireless telephone plan is $39.99 for up to 450 min of calling time plus $0.45 per minute for each minute over 450 min. The equation that describes the cost of this plan is C = 0.45x + 39.99,

 where x is the number of minutes over 450. What is the cost of this plan if a person uses 382 min and 471 min of calling time?

Answer 1

The monthly cost of a wireless telephone plan is $39.99 for up to 450 min of calling time plus $0.45 per minute for each minute over 450 min. The equation that describes the cost of this plan is C(x) = 0.45x + 39.99; where x is the number of minutes over 450: x = t - 450.

C(x) = 0.45x + 39.99 ==> C(t) = 0.45(t - 450) + 39.99

C(t) = 39.99 for t - 450 ≤ 0

C(t) = 0.45(t - 450) + 39.99 for t - 450 > 0

What is the cost of this plan if a person uses 382 min and 471 min of calling time?

a) t = 382 min ==> t - 450 min ==> 382 min - 450 min ==> -68 min ==> t - 450 < 0

C(382) = $39.99 <== Cost if a person uses 382 min

b) t = 471 min ==> t - 450 min ==> 471 min - 450 min ==> 21 min ==> t - 450 > 0

C(t) = 0.45(t - 450) + 39.99 ==> C(471) = 0.45(471 - 450) + 39.99 ==> C(471) = 0.45(21) + 39.99 ==> C(471) = 9.45 + 39.99 ==> C(471) = $49.44

C(471) = $49.44 <== Cost if a person uses 471 min

Answer 2

In order to use the provided function C = 0.45x + 39.99, you must estimate how many minutes over 450min the person used.

Total minutes: 853

Minutes permitted for flat rate of $39.99: 450

minutes over 450: 402

Of the total 853 minutes the person used, 450 of them are accounted for in the flat rate of $39.99.

The remaining 402 minutes over will cost an additional $0.45/min.

Therefore, to determine the cost for the month, only use 402 minutes

_{for 450 min}

C = $0.45(402min) + $39.99 = $220.89 :-O

min

^{notice: when adding, you can only combine like terms. Once you've cancelled the minute units from the numerator and denominator of the first term, the only unit that remains is $, which matches the unit of the second term, thus allowing you to combine them.}