Albert Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 60 minutes of talk time for $19.80. Plan B offers 300 SMS and 170 minutes of talk time for $32.10. Albert Mobile Company is also going to launch Plan C which offers 170 SMS and 220 minutes of talk time. How much should Albert 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 = 200 SMS + 60 min = 1980 --- (1)

Plan B = 300 SMS + 170 min = 3210 --- (2)

Make the cost of SMS the same.

(1)_x3
600 SMS + 180 min = 5940 --- (3)

(2)_x2
600 SMS + 340 min = 6420 --- (4)

(4) - (3)
340 min - 180 min = 6420 - 5940
160 min = 480

1 min = 480 ÷ 160 = 3

60 min = 60 x 3 = 180

From (1):
200 SMS + 60 min = 1980 
200 SMS + 60 x 3 = 1980
200 SMS + 180 = 1980
200 SMS = 1980 - 180
200 SMS = 1800

1 SMS = 1800 ÷ 200 = 9

170 SMS
= 170 x 9
= 1530

220 min
= 220 x 3
= 660

Charges for Plan C
= 170 SMS + 220 min
= 1530 + 660
= 2190¢

2190¢ = 2190 ÷ 100 = $21.90

Answer(s): $21.90