Sean Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 50 minutes of talk time for $13.50. Plan B offers 210 SMS and 140 minutes of talk time for $25.20. Sean Mobile Company is also going to launch Plan C which offers 190 SMS and 240 minutes of talk time. How much should Sean 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 = 120 SMS + 50 min = 1350 --- (1)

Plan B = 210 SMS + 140 min = 2520 --- (2)

Make the cost of SMS the same.

(1)_x7
840 SMS + 350 min = 9450 --- (3)

(2)_x4
840 SMS + 560 min = 10080 --- (4)

(4) - (3)
560 min - 350 min = 10080 - 9450
210 min = 630

1 min = 630 ÷ 210 = 3

50 min = 50 x 3 = 150

From (1):
120 SMS + 50 min = 1350 
120 SMS + 50 x 3 = 1350
120 SMS + 150 = 1350
120 SMS = 1350 - 150
120 SMS = 1200

1 SMS = 1200 ÷ 120 = 10

190 SMS
= 190 x 10
= 1900

240 min
= 240 x 3
= 720

Charges for Plan C
= 190 SMS + 240 min
= 1900 + 720
= 2620¢

2620¢ = 2620 ÷ 100 = $26.20

Answer(s): $26.20