Luis Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 60 minutes of talk time for $17.20. Plan B offers 400 SMS and 180 minutes of talk time for $43.60. Luis Mobile Company is also going to launch Plan C which offers 180 SMS and 240 minutes of talk time. How much should Luis 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 + 60 min = 1720 --- (1)

Plan B = 400 SMS + 180 min = 4360 --- (2)

Make the cost of SMS the same.

(1)_x5
800 SMS + 300 min = 8600 --- (3)

(2)_x2
800 SMS + 360 min = 8720 --- (4)

(4) - (3)
360 min - 300 min = 8720 - 8600
60 min = 120

1 min = 120 ÷ 60 = 2

60 min = 60 x 2 = 120

From (1):
160 SMS + 60 min = 1720 
160 SMS + 60 x 2 = 1720
160 SMS + 120 = 1720
160 SMS = 1720 - 120
160 SMS = 1600

1 SMS = 1600 ÷ 160 = 10

180 SMS
= 180 x 10
= 1800

240 min
= 240 x 2
= 480

Charges for Plan C
= 180 SMS + 240 min
= 1800 + 480
= 2280¢

2280¢ = 2280 ÷ 100 = $22.80

Answer(s): $22.80