Nick Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 90 minutes of talk time for $22.70. Plan B offers 300 SMS and 140 minutes of talk time for $28.20. Nick Mobile Company is also going to launch Plan C which offers 120 SMS and 270 minutes of talk time. How much should Nick 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 + 90 min = 2270 --- (1)

Plan B = 300 SMS + 140 min = 2820 --- (2)

Make the cost of SMS the same.

(1)_x6
1500 SMS + 540 min = 13620 --- (3)

(2)_x5
1500 SMS + 700 min = 14100 --- (4)

(4) - (3)
700 min - 540 min = 14100 - 13620
160 min = 480

1 min = 480 ÷ 160 = 3

90 min = 90 x 3 = 270

From (1):
250 SMS + 90 min = 2270 
250 SMS + 90 x 3 = 2270
250 SMS + 270 = 2270
250 SMS = 2270 - 270
250 SMS = 2000

1 SMS = 2000 ÷ 250 = 8

120 SMS
= 120 x 8
= 960

270 min
= 270 x 3
= 810

Charges for Plan C
= 120 SMS + 270 min
= 960 + 810
= 1770¢

1770¢ = 1770 ÷ 100 = $17.70

Answer(s): $17.70