Owen Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 50 minutes of talk time for $11.50. Plan B offers 270 SMS and 130 minutes of talk time for $21.50. Owen Mobile Company is also going to launch Plan C which offers 180 SMS and 210 minutes of talk time. How much should Owen 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 = 1150 --- (1)

Plan B = 270 SMS + 130 min = 2150 --- (2)

Make the cost of SMS the same.

(1)_x9
1350 SMS + 450 min = 10350 --- (3)

(2)_x5
1350 SMS + 650 min = 10750 --- (4)

(4) - (3)
650 min - 450 min = 10750 - 10350
200 min = 400

1 min = 400 ÷ 200 = 2

50 min = 50 x 2 = 100

From (1):
150 SMS + 50 min = 1150 
150 SMS + 50 x 2 = 1150
150 SMS + 100 = 1150
150 SMS = 1150 - 100
150 SMS = 1050

1 SMS = 1050 ÷ 150 = 7

180 SMS
= 180 x 7
= 1260

210 min
= 210 x 2
= 420

Charges for Plan C
= 180 SMS + 210 min
= 1260 + 420
= 1680¢

1680¢ = 1680 ÷ 100 = $16.80

Answer(s): $16.80