Henry 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 180 SMS and 190 minutes of talk time for $16.60. Henry Mobile Company is also going to launch Plan C which offers 160 SMS and 220 minutes of talk time. How much should Henry 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 = 180 SMS + 190 min = 1660 --- (2)

Make the cost of SMS the same.

(1)_x6
900 SMS + 420 min = 6180 --- (3)

(2)_x5
900 SMS + 950 min = 8300 --- (4)

(4) - (3)
950 min - 420 min = 8300 - 6180
530 min = 2120

1 min = 2120 ÷ 530 = 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

160 SMS
= 160 x 5
= 800

220 min
= 220 x 4
= 880

Charges for Plan C
= 160 SMS + 220 min
= 800 + 880
= 1680¢

1680¢ = 1680 ÷ 100 = $16.80

Answer(s): $16.80