Daniel Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 60 minutes of talk time for $8.40. Plan B offers 180 SMS and 160 minutes of talk time for $15.40. Daniel Mobile Company is also going to launch Plan C which offers 150 SMS and 290 minutes of talk time. How much should Daniel 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 = 120 SMS + 60 min = 840 --- (1)

Plan B = 180 SMS + 160 min = 1540 --- (2)

Make the cost of SMS the same.

(1)_x3
360 SMS + 180 min = 2520 --- (3)

(2)_x2
360 SMS + 320 min = 3080 --- (4)

(4) - (3)
320 min - 180 min = 3080 - 2520
140 min = 560

1 min = 560 ÷ 140 = 4

60 min = 60 x 4 = 240

From (1):
120 SMS + 60 min = 840 
120 SMS + 60 x 4 = 840
120 SMS + 240 = 840
120 SMS = 840 - 240
120 SMS = 600

1 SMS = 600 ÷ 120 = 5

150 SMS
= 150 x 5
= 750

290 min
= 290 x 4
= 1160

Charges for Plan C
= 150 SMS + 290 min
= 750 + 1160
= 1910¢

1910¢ = 1910 ÷ 100 = $19.10

Answer(s): $19.10