Riordan Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 80 minutes of talk time for $17.40. Plan B offers 400 SMS and 170 minutes of talk time for $29.10. Riordan Mobile Company is also going to launch Plan C which offers 120 SMS and 200 minutes of talk time. How much should Riordan 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 = 250 SMS + 80 min = 1740 --- (1)

Plan B = 400 SMS + 170 min = 2910 --- (2)

Make the cost of SMS the same.

(1)_x8
2000 SMS + 640 min = 13920 --- (3)

(2)_x5
2000 SMS + 850 min = 14550 --- (4)

(4) - (3)
850 min - 640 min = 14550 - 13920
210 min = 630

1 min = 630 ÷ 210 = 3

80 min = 80 x 3 = 240

From (1):
250 SMS + 80 min = 1740 
250 SMS + 80 x 3 = 1740
250 SMS + 240 = 1740
250 SMS = 1740 - 240
250 SMS = 1500

1 SMS = 1500 ÷ 250 = 6

120 SMS
= 120 x 6
= 720

200 min
= 200 x 3
= 600

Charges for Plan C
= 120 SMS + 200 min
= 720 + 600
= 1320¢

1320¢ = 1320 ÷ 100 = $13.20

Answer(s): $13.20