Lee Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 80 minutes of talk time for $11.40. Plan B offers 240 SMS and 140 minutes of talk time for $18.60. Lee Mobile Company is also going to launch Plan C which offers 170 SMS and 300 minutes of talk time. How much should Lee 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 = 150 SMS + 80 min = 1140 --- (1)

Plan B = 240 SMS + 140 min = 1860 --- (2)

Make the cost of SMS the same.

(1)_x8
1200 SMS + 640 min = 9120 --- (3)

(2)_x5
1200 SMS + 700 min = 9300 --- (4)

(4) - (3)
700 min - 640 min = 9300 - 9120
60 min = 180

1 min = 180 ÷ 60 = 3

80 min = 80 x 3 = 240

From (1):
150 SMS + 80 min = 1140 
150 SMS + 80 x 3 = 1140
150 SMS + 240 = 1140
150 SMS = 1140 - 240
150 SMS = 900

1 SMS = 900 ÷ 150 = 6

170 SMS
= 170 x 6
= 1020

300 min
= 300 x 3
= 900

Charges for Plan C
= 170 SMS + 300 min
= 1020 + 900
= 1920¢

1920¢ = 1920 ÷ 100 = $19.20

Answer(s): $19.20