Howard Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 50 minutes of talk time for $11.10. Plan B offers 240 SMS and 100 minutes of talk time for $17.40. Howard Mobile Company is also going to launch Plan C which offers 130 SMS and 280 minutes of talk time. How much should Howard 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 = 1110 --- (1)

Plan B = 240 SMS + 100 min = 1740 --- (2)

Make the cost of SMS the same.

(1)_x3
480 SMS + 150 min = 3330 --- (3)

(2)_x2
480 SMS + 200 min = 3480 --- (4)

(4) - (3)
200 min - 150 min = 3480 - 3330
50 min = 150

1 min = 150 ÷ 50 = 3

50 min = 50 x 3 = 150

From (1):
160 SMS + 50 min = 1110 
160 SMS + 50 x 3 = 1110
160 SMS + 150 = 1110
160 SMS = 1110 - 150
160 SMS = 960

1 SMS = 960 ÷ 160 = 6

130 SMS
= 130 x 6
= 780

280 min
= 280 x 3
= 840

Charges for Plan C
= 130 SMS + 280 min
= 780 + 840
= 1620¢

1620¢ = 1620 ÷ 100 = $16.20

Answer(s): $16.20