Xavier Mobile Company has a few mobile phone service plans. Plan A offers 80 SMS and 50 minutes of talk time for $6.30. Plan B offers 280 SMS and 180 minutes of talk time for $22.20. Xavier Mobile Company is also going to launch Plan C which offers 170 SMS and 270 minutes of talk time. How much should Xavier 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 = 80 SMS + 50 min = 630 --- (1)

Plan B = 280 SMS + 180 min = 2220 --- (2)

Make the cost of SMS the same.

(1)_x7
560 SMS + 350 min = 4410 --- (3)

(2)_x2
560 SMS + 360 min = 4440 --- (4)

(4) - (3)
360 min - 350 min = 4440 - 4410
10 min = 30

1 min = 30 ÷ 10 = 3

50 min = 50 x 3 = 150

From (1):
80 SMS + 50 min = 630 
80 SMS + 50 x 3 = 630
80 SMS + 150 = 630
80 SMS = 630 - 150
80 SMS = 480

1 SMS = 480 ÷ 80 = 6

170 SMS
= 170 x 6
= 1020

270 min
= 270 x 3
= 810

Charges for Plan C
= 170 SMS + 270 min
= 1020 + 810
= 1830¢

1830¢ = 1830 ÷ 100 = $18.30

Answer(s): $18.30