Owen 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 190 minutes of talk time for $24.90. Owen Mobile Company is also going to launch Plan C which offers 150 SMS and 250 minutes of talk time. How much should Owen 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 + 190 min = 2490 --- (2)

Make the cost of SMS the same.

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

(2)_x5
1200 SMS + 950 min = 12450 --- (4)

(4) - (3)
950 min - 400 min = 12450 - 10800
550 min = 1650

1 min = 1650 ÷ 550 = 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

150 SMS
= 150 x 8
= 1200

250 min
= 250 x 3
= 750

Charges for Plan C
= 150 SMS + 250 min
= 1200 + 750
= 1950¢

1950¢ = 1950 ÷ 100 = $19.50

Answer(s): $19.50