Ahmad Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 60 minutes of talk time for $13.80. Plan B offers 300 SMS and 160 minutes of talk time for $22.80. Ahmad Mobile Company is also going to launch Plan C which offers 170 SMS and 230 minutes of talk time. How much should Ahmad 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 = 200 SMS + 60 min = 1380 --- (1)

Plan B = 300 SMS + 160 min = 2280 --- (2)

Make the cost of SMS the same.

(1)_x3
600 SMS + 180 min = 4140 --- (3)

(2)_x2
600 SMS + 320 min = 4560 --- (4)

(4) - (3)
320 min - 180 min = 4560 - 4140
140 min = 420

1 min = 420 ÷ 140 = 3

60 min = 60 x 3 = 180

From (1):
200 SMS + 60 min = 1380 
200 SMS + 60 x 3 = 1380
200 SMS + 180 = 1380
200 SMS = 1380 - 180
200 SMS = 1200

1 SMS = 1200 ÷ 200 = 6

170 SMS
= 170 x 6
= 1020

230 min
= 230 x 3
= 690

Charges for Plan C
= 170 SMS + 230 min
= 1020 + 690
= 1710¢

1710¢ = 1710 ÷ 100 = $17.10

Answer(s): $17.10