Seth Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 80 minutes of talk time for $10.60. Plan B offers 210 SMS and 140 minutes of talk time for $15.40. Seth Mobile Company is also going to launch Plan C which offers 120 SMS and 280 minutes of talk time. How much should Seth 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 + 80 min = 1060 --- (1)

Plan B = 210 SMS + 140 min = 1540 --- (2)

Make the cost of SMS the same.

(1)_x7
1050 SMS + 560 min = 7420 --- (3)

(2)_x5
1050 SMS + 700 min = 7700 --- (4)

(4) - (3)
700 min - 560 min = 7700 - 7420
140 min = 280

1 min = 280 ÷ 140 = 2

80 min = 80 x 2 = 160

From (1):
150 SMS + 80 min = 1060 
150 SMS + 80 x 2 = 1060
150 SMS + 160 = 1060
150 SMS = 1060 - 160
150 SMS = 900

1 SMS = 900 ÷ 150 = 6

120 SMS
= 120 x 6
= 720

280 min
= 280 x 2
= 560

Charges for Plan C
= 120 SMS + 280 min
= 720 + 560
= 1280¢

1280¢ = 1280 ÷ 100 = $12.80

Answer(s): $12.80