Reggie Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 70 minutes of talk time for $27.80. Plan B offers 300 SMS and 120 minutes of talk time for $34.80. Reggie Mobile Company is also going to launch Plan C which offers 120 SMS and 220 minutes of talk time. How much should Reggie 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 = 250 SMS + 70 min = 2780 --- (1)

Plan B = 300 SMS + 120 min = 3480 --- (2)

Make the cost of SMS the same.

(1)_x6
1500 SMS + 420 min = 16680 --- (3)

(2)_x5
1500 SMS + 600 min = 17400 --- (4)

(4) - (3)
600 min - 420 min = 17400 - 16680
180 min = 720

1 min = 720 ÷ 180 = 4

70 min = 70 x 4 = 280

From (1):
250 SMS + 70 min = 2780 
250 SMS + 70 x 4 = 2780
250 SMS + 280 = 2780
250 SMS = 2780 - 280
250 SMS = 2500

1 SMS = 2500 ÷ 250 = 10

120 SMS
= 120 x 10
= 1200

220 min
= 220 x 4
= 880

Charges for Plan C
= 120 SMS + 220 min
= 1200 + 880
= 2080¢

2080¢ = 2080 ÷ 100 = $20.80

Answer(s): $20.80