Archie Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 60 minutes of talk time for $12.30. Plan B offers 210 SMS and 190 minutes of talk time for $20.40. Archie Mobile Company is also going to launch Plan C which offers 140 SMS and 250 minutes of talk time. How much should Archie 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 = 150 SMS + 60 min = 1230 --- (1)

Plan B = 210 SMS + 190 min = 2040 --- (2)

Make the cost of SMS the same.

(1)_x7
1050 SMS + 420 min = 8610 --- (3)

(2)_x5
1050 SMS + 950 min = 10200 --- (4)

(4) - (3)
950 min - 420 min = 10200 - 8610
530 min = 1590

1 min = 1590 ÷ 530 = 3

60 min = 60 x 3 = 180

From (1):
150 SMS + 60 min = 1230 
150 SMS + 60 x 3 = 1230
150 SMS + 180 = 1230
150 SMS = 1230 - 180
150 SMS = 1050

1 SMS = 1050 ÷ 150 = 7

140 SMS
= 140 x 7
= 980

250 min
= 250 x 3
= 750

Charges for Plan C
= 140 SMS + 250 min
= 980 + 750
= 1730¢

1730¢ = 1730 ÷ 100 = $17.30

Answer(s): $17.30