Simon Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 70 minutes of talk time for $16.30. Plan B offers 180 SMS and 110 minutes of talk time for $20.60. Simon Mobile Company is also going to launch Plan C which offers 160 SMS and 270 minutes of talk time. How much should Simon 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 + 70 min = 1630 --- (1)

Plan B = 180 SMS + 110 min = 2060 --- (2)

Make the cost of SMS the same.

(1)_x6
900 SMS + 420 min = 9780 --- (3)

(2)_x5
900 SMS + 550 min = 10300 --- (4)

(4) - (3)
550 min - 420 min = 10300 - 9780
130 min = 520

1 min = 520 ÷ 130 = 4

70 min = 70 x 4 = 280

From (1):
150 SMS + 70 min = 1630 
150 SMS + 70 x 4 = 1630
150 SMS + 280 = 1630
150 SMS = 1630 - 280
150 SMS = 1350

1 SMS = 1350 ÷ 150 = 9

160 SMS
= 160 x 9
= 1440

270 min
= 270 x 4
= 1080

Charges for Plan C
= 160 SMS + 270 min
= 1440 + 1080
= 2520¢

2520¢ = 2520 ÷ 100 = $25.20

Answer(s): $25.20