Jeremy Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 50 minutes of talk time for $12.70. Plan B offers 240 SMS and 180 minutes of talk time for $22.20. Jeremy Mobile Company is also going to launch Plan C which offers 160 SMS and 210 minutes of talk time. How much should Jeremy 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 = 1270 --- (1)

Plan B = 240 SMS + 180 min = 2220 --- (2)

Make the cost of SMS the same.

(1)_x3
480 SMS + 150 min = 3810 --- (3)

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

(4) - (3)
360 min - 150 min = 4440 - 3810
210 min = 630

1 min = 630 ÷ 210 = 3

50 min = 50 x 3 = 150

From (1):
160 SMS + 50 min = 1270 
160 SMS + 50 x 3 = 1270
160 SMS + 150 = 1270
160 SMS = 1270 - 150
160 SMS = 1120

1 SMS = 1120 ÷ 160 = 7

160 SMS
= 160 x 7
= 1120

210 min
= 210 x 3
= 630

Charges for Plan C
= 160 SMS + 210 min
= 1120 + 630
= 1750¢

1750¢ = 1750 ÷ 100 = $17.50

Answer(s): $17.50