David Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 60 minutes of talk time for $19.80. Plan B offers 450 SMS and 160 minutes of talk time for $45.30. David Mobile Company is also going to launch Plan C which offers 120 SMS and 300 minutes of talk time. How much should David 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 = 200 SMS + 60 min = 1980 --- (1)

Plan B = 450 SMS + 160 min = 4530 --- (2)

Make the cost of SMS the same.

(1)_x9
1800 SMS + 540 min = 17820 --- (3)

(2)_x4
1800 SMS + 640 min = 18120 --- (4)

(4) - (3)
640 min - 540 min = 18120 - 17820
100 min = 300

1 min = 300 ÷ 100 = 3

60 min = 60 x 3 = 180

From (1):
200 SMS + 60 min = 1980 
200 SMS + 60 x 3 = 1980
200 SMS + 180 = 1980
200 SMS = 1980 - 180
200 SMS = 1800

1 SMS = 1800 ÷ 200 = 9

120 SMS
= 120 x 9
= 1080

300 min
= 300 x 3
= 900

Charges for Plan C
= 120 SMS + 300 min
= 1080 + 900
= 1980¢

1980¢ = 1980 ÷ 100 = $19.80

Answer(s): $19.80