Warren Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 50 minutes of talk time for $13.50. Plan B offers 240 SMS and 140 minutes of talk time for $23.40. Warren Mobile Company is also going to launch Plan C which offers 130 SMS and 270 minutes of talk time. How much should Warren 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 = 1350 --- (1)

Plan B = 240 SMS + 140 min = 2340 --- (2)

Make the cost of SMS the same.

(1)_x8
1200 SMS + 400 min = 10800 --- (3)

(2)_x5
1200 SMS + 700 min = 11700 --- (4)

(4) - (3)
700 min - 400 min = 11700 - 10800
300 min = 900

1 min = 900 ÷ 300 = 3

50 min = 50 x 3 = 150

From (1):
150 SMS + 50 min = 1350 
150 SMS + 50 x 3 = 1350
150 SMS + 150 = 1350
150 SMS = 1350 - 150
150 SMS = 1200

1 SMS = 1200 ÷ 150 = 8

130 SMS
= 130 x 8
= 1040

270 min
= 270 x 3
= 810

Charges for Plan C
= 130 SMS + 270 min
= 1040 + 810
= 1850¢

1850¢ = 1850 ÷ 100 = $18.50

Answer(s): $18.50