Peter Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 50 minutes of talk time for $8.50. Plan B offers 180 SMS and 190 minutes of talk time for $12.80. Peter Mobile Company is also going to launch Plan C which offers 190 SMS and 290 minutes of talk time. How much should Peter Mobile Company charge for Plan C if the cost per SMS and the cost per minute of talk time do not vary across the three plans?
$1 = 100¢

Plan A = 150 SMS + 50 min = 850 --- (1)

Plan B = 180 SMS + 190 min = 1280 --- (2)

Make the cost of SMS the same.

(1)_x6
900 SMS + 300 min = 5100 --- (3)

(2)_x5
900 SMS + 950 min = 6400 --- (4)

(4) - (3)
950 min - 300 min = 6400 - 5100
650 min = 1300

1 min = 1300 ÷ 650 = 2

50 min = 50 x 2 = 100

From (1):
150 SMS + 50 min = 850 
150 SMS + 50 x 2 = 850
150 SMS + 100 = 850
150 SMS = 850 - 100
150 SMS = 750

1 SMS = 750 ÷ 150 = 5

190 SMS
= 190 x 5
= 950

290 min
= 290 x 2
= 580

Charges for Plan C
= 190 SMS + 290 min
= 950 + 580
= 1530¢

1530¢ = 1530 ÷ 100 = $15.30

Answer(s): $15.30