Caden Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 50 minutes of talk time for $12.80. Plan B offers 270 SMS and 140 minutes of talk time for $29.90. Caden Mobile Company is also going to launch Plan C which offers 170 SMS and 230 minutes of talk time. How much should Caden 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 = 1280 --- (1)

Plan B = 270 SMS + 140 min = 2990 --- (2)

Make the cost of SMS the same.

(1)_x9
1080 SMS + 450 min = 11520 --- (3)

(2)_x4
1080 SMS + 560 min = 11960 --- (4)

(4) - (3)
560 min - 450 min = 11960 - 11520
110 min = 440

1 min = 440 ÷ 110 = 4

50 min = 50 x 4 = 200

From (1):
120 SMS + 50 min = 1280 
120 SMS + 50 x 4 = 1280
120 SMS + 200 = 1280
120 SMS = 1280 - 200
120 SMS = 1080

1 SMS = 1080 ÷ 120 = 9

170 SMS
= 170 x 9
= 1530

230 min
= 230 x 4
= 920

Charges for Plan C
= 170 SMS + 230 min
= 1530 + 920
= 2450¢

2450¢ = 2450 ÷ 100 = $24.50

Answer(s): $24.50