Vincent Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 80 minutes of talk time for $26.60. Plan B offers 350 SMS and 120 minutes of talk time for $37.40. Vincent Mobile Company is also going to launch Plan C which offers 160 SMS and 210 minutes of talk time. How much should Vincent 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 = 250 SMS + 80 min = 2660 --- (1)

Plan B = 350 SMS + 120 min = 3740 --- (2)

Make the cost of SMS the same.

(1)_x7
1750 SMS + 560 min = 18620 --- (3)

(2)_x5
1750 SMS + 600 min = 18700 --- (4)

(4) - (3)
600 min - 560 min = 18700 - 18620
40 min = 80

1 min = 80 ÷ 40 = 2

80 min = 80 x 2 = 160

From (1):
250 SMS + 80 min = 2660 
250 SMS + 80 x 2 = 2660
250 SMS + 160 = 2660
250 SMS = 2660 - 160
250 SMS = 2500

1 SMS = 2500 ÷ 250 = 10

160 SMS
= 160 x 10
= 1600

210 min
= 210 x 2
= 420

Charges for Plan C
= 160 SMS + 210 min
= 1600 + 420
= 2020¢

2020¢ = 2020 ÷ 100 = $20.20

Answer(s): $20.20