Cody Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 60 minutes of talk time for $13.70. Plan B offers 350 SMS and 170 minutes of talk time for $20.90. Cody Mobile Company is also going to launch Plan C which offers 150 SMS and 260 minutes of talk time. How much should Cody 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 + 60 min = 1370 --- (1)

Plan B = 350 SMS + 170 min = 2090 --- (2)

Make the cost of SMS the same.

(1)_x7
1750 SMS + 420 min = 9590 --- (3)

(2)_x5
1750 SMS + 850 min = 10450 --- (4)

(4) - (3)
850 min - 420 min = 10450 - 9590
430 min = 860

1 min = 860 ÷ 430 = 2

60 min = 60 x 2 = 120

From (1):
250 SMS + 60 min = 1370 
250 SMS + 60 x 2 = 1370
250 SMS + 120 = 1370
250 SMS = 1370 - 120
250 SMS = 1250

1 SMS = 1250 ÷ 250 = 5

150 SMS
= 150 x 5
= 750

260 min
= 260 x 2
= 520

Charges for Plan C
= 150 SMS + 260 min
= 750 + 520
= 1270¢

1270¢ = 1270 ÷ 100 = $12.70

Answer(s): $12.70