Vincent Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 50 minutes of talk time for $14.50. Plan B offers 500 SMS and 180 minutes of talk time for $48.60. Vincent Mobile Company is also going to launch Plan C which offers 160 SMS and 260 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 = 150 SMS + 50 min = 1450 --- (1)

Plan B = 500 SMS + 180 min = 4860 --- (2)

Make the cost of SMS the same.

(1)_x10
1500 SMS + 500 min = 14500 --- (3)

(2)_x3
1500 SMS + 540 min = 14580 --- (4)

(4) - (3)
540 min - 500 min = 14580 - 14500
40 min = 80

1 min = 80 ÷ 40 = 2

50 min = 50 x 2 = 100

From (1):
150 SMS + 50 min = 1450 
150 SMS + 50 x 2 = 1450
150 SMS + 100 = 1450
150 SMS = 1450 - 100
150 SMS = 1350

1 SMS = 1350 ÷ 150 = 9

160 SMS
= 160 x 9
= 1440

260 min
= 260 x 2
= 520

Charges for Plan C
= 160 SMS + 260 min
= 1440 + 520
= 1960¢

1960¢ = 1960 ÷ 100 = $19.60

Answer(s): $19.60