Zane Mobile Company has a few mobile phone service plans. Plan A offers 90 SMS and 60 minutes of talk time for $6.90. Plan B offers 210 SMS and 150 minutes of talk time for $16.50. Zane Mobile Company is also going to launch Plan C which offers 160 SMS and 220 minutes of talk time. How much should Zane 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 = 90 SMS + 60 min = 690 --- (1)

Plan B = 210 SMS + 150 min = 1650 --- (2)

Make the cost of SMS the same.

(1)_x7
630 SMS + 420 min = 4830 --- (3)

(2)_x3
630 SMS + 450 min = 4950 --- (4)

(4) - (3)
450 min - 420 min = 4950 - 4830
30 min = 120

1 min = 120 ÷ 30 = 4

60 min = 60 x 4 = 240

From (1):
90 SMS + 60 min = 690 
90 SMS + 60 x 4 = 690
90 SMS + 240 = 690
90 SMS = 690 - 240
90 SMS = 450

1 SMS = 450 ÷ 90 = 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