Vaidev Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 50 minutes of talk time for $21.50. Plan B offers 450 SMS and 180 minutes of talk time for $41.40. Vaidev Mobile Company is also going to launch Plan C which offers 140 SMS and 270 minutes of talk time. How much should Vaidev 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 + 50 min = 2150 --- (1)

Plan B = 450 SMS + 180 min = 4140 --- (2)

Make the cost of SMS the same.

(1)_x9
2250 SMS + 450 min = 19350 --- (3)

(2)_x5
2250 SMS + 900 min = 20700 --- (4)

(4) - (3)
900 min - 450 min = 20700 - 19350
450 min = 1350

1 min = 1350 ÷ 450 = 3

50 min = 50 x 3 = 150

From (1):
250 SMS + 50 min = 2150 
250 SMS + 50 x 3 = 2150
250 SMS + 150 = 2150
250 SMS = 2150 - 150
250 SMS = 2000

1 SMS = 2000 ÷ 250 = 8

140 SMS
= 140 x 8
= 1120

270 min
= 270 x 3
= 810

Charges for Plan C
= 140 SMS + 270 min
= 1120 + 810
= 1930¢

1930¢ = 1930 ÷ 100 = $19.30

Answer(s): $19.30