Nick Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 50 minutes of talk time for $13.50. Plan B offers 300 SMS and 160 minutes of talk time for $22.80. Nick Mobile Company is also going to launch Plan C which offers 190 SMS and 200 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 = 200 SMS + 50 min = 1350 --- (1)

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

Make the cost of SMS the same.

(1)_x3
600 SMS + 150 min = 4050 --- (3)

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

(4) - (3)
320 min - 150 min = 4560 - 4050
170 min = 510

1 min = 510 ÷ 170 = 3

50 min = 50 x 3 = 150

From (1):
200 SMS + 50 min = 1350 
200 SMS + 50 x 3 = 1350
200 SMS + 150 = 1350
200 SMS = 1350 - 150
200 SMS = 1200

1 SMS = 1200 ÷ 200 = 6

190 SMS
= 190 x 6
= 1140

200 min
= 200 x 3
= 600

Charges for Plan C
= 190 SMS + 200 min
= 1140 + 600
= 1740¢

1740¢ = 1740 ÷ 100 = $17.40

Answer(s): $17.40