Cody Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 50 minutes of talk time for $14.80. Plan B offers 400 SMS and 160 minutes of talk time for $38.40. Cody Mobile Company is also going to launch Plan C which offers 130 SMS and 260 minutes of talk time. How much should Cody 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 + 50 min = 1480 --- (1)

Plan B = 400 SMS + 160 min = 3840 --- (2)

Make the cost of SMS the same.

(1)_x5
800 SMS + 250 min = 7400 --- (3)

(2)_x2
800 SMS + 320 min = 7680 --- (4)

(4) - (3)
320 min - 250 min = 7680 - 7400
70 min = 280

1 min = 280 ÷ 70 = 4

50 min = 50 x 4 = 200

From (1):
160 SMS + 50 min = 1480 
160 SMS + 50 x 4 = 1480
160 SMS + 200 = 1480
160 SMS = 1480 - 200
160 SMS = 1280

1 SMS = 1280 ÷ 160 = 8

130 SMS
= 130 x 8
= 1040

260 min
= 260 x 4
= 1040

Charges for Plan C
= 130 SMS + 260 min
= 1040 + 1040
= 2080¢

2080¢ = 2080 ÷ 100 = $20.80

Answer(s): $20.80