Howard Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 70 minutes of talk time for $10.30. Plan B offers 270 SMS and 130 minutes of talk time for $18.70. Howard Mobile Company is also going to launch Plan C which offers 170 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 = 150 SMS + 70 min = 1030 --- (1)

Plan B = 270 SMS + 130 min = 1870 --- (2)

Make the cost of SMS the same.

(1)_x9
1350 SMS + 630 min = 9270 --- (3)

(2)_x5
1350 SMS + 650 min = 9350 --- (4)

(4) - (3)
650 min - 630 min = 9350 - 9270
20 min = 80

1 min = 80 ÷ 20 = 4

70 min = 70 x 4 = 280

From (1):
150 SMS + 70 min = 1030 
150 SMS + 70 x 4 = 1030
150 SMS + 280 = 1030
150 SMS = 1030 - 280
150 SMS = 750

1 SMS = 750 ÷ 150 = 5

170 SMS
= 170 x 5
= 850

280 min
= 280 x 4
= 1120

Charges for Plan C
= 170 SMS + 280 min
= 850 + 1120
= 1970¢

1970¢ = 1970 ÷ 100 = $19.70

Answer(s): $19.70