Rael Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 70 minutes of talk time for $17.10. Plan B offers 210 SMS and 180 minutes of talk time for $26.40. Rael Mobile Company is also going to launch Plan C which offers 170 SMS and 290 minutes of talk time. How much should Rael 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 + 70 min = 1710 --- (1)

Plan B = 210 SMS + 180 min = 2640 --- (2)

Make the cost of SMS the same.

(1)_x7
1050 SMS + 490 min = 11970 --- (3)

(2)_x5
1050 SMS + 900 min = 13200 --- (4)

(4) - (3)
900 min - 490 min = 13200 - 11970
410 min = 1230

1 min = 1230 ÷ 410 = 3

70 min = 70 x 3 = 210

From (1):
150 SMS + 70 min = 1710 
150 SMS + 70 x 3 = 1710
150 SMS + 210 = 1710
150 SMS = 1710 - 210
150 SMS = 1500

1 SMS = 1500 ÷ 150 = 10

170 SMS
= 170 x 10
= 1700

290 min
= 290 x 3
= 870

Charges for Plan C
= 170 SMS + 290 min
= 1700 + 870
= 2570¢

2570¢ = 2570 ÷ 100 = $25.70

Answer(s): $25.70