Fabian Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 50 minutes of talk time for $15.40. Plan B offers 400 SMS and 130 minutes of talk time for $38.60. Fabian Mobile Company is also going to launch Plan C which offers 150 SMS and 200 minutes of talk time. How much should Fabian 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 = 160 SMS + 50 min = 1540 --- (1)

Plan B = 400 SMS + 130 min = 3860 --- (2)

Make the cost of SMS the same.

(1)_x5
800 SMS + 250 min = 7700 --- (3)

(2)_x2
800 SMS + 260 min = 7720 --- (4)

(4) - (3)
260 min - 250 min = 7720 - 7700
10 min = 20

1 min = 20 ÷ 10 = 2

50 min = 50 x 2 = 100

From (1):
160 SMS + 50 min = 1540 
160 SMS + 50 x 2 = 1540
160 SMS + 100 = 1540
160 SMS = 1540 - 100
160 SMS = 1440

1 SMS = 1440 ÷ 160 = 9

150 SMS
= 150 x 9
= 1350

200 min
= 200 x 2
= 400

Charges for Plan C
= 150 SMS + 200 min
= 1350 + 400
= 1750¢

1750¢ = 1750 ÷ 100 = $17.50

Answer(s): $17.50