Gabriel Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 50 minutes of talk time for $18.50. Plan B offers 400 SMS and 120 minutes of talk time for $30.40. Gabriel Mobile Company is also going to launch Plan C which offers 130 SMS and 270 minutes of talk time. How much should Gabriel 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 + 50 min = 1850 --- (1)

Plan B = 400 SMS + 120 min = 3040 --- (2)

Make the cost of SMS the same.

(1)_x8
2000 SMS + 400 min = 14800 --- (3)

(2)_x5
2000 SMS + 600 min = 15200 --- (4)

(4) - (3)
600 min - 400 min = 15200 - 14800
200 min = 400

1 min = 400 ÷ 200 = 2

50 min = 50 x 2 = 100

From (1):
250 SMS + 50 min = 1850 
250 SMS + 50 x 2 = 1850
250 SMS + 100 = 1850
250 SMS = 1850 - 100
250 SMS = 1750

1 SMS = 1750 ÷ 250 = 7

130 SMS
= 130 x 7
= 910

270 min
= 270 x 2
= 540

Charges for Plan C
= 130 SMS + 270 min
= 910 + 540
= 1450¢

1450¢ = 1450 ÷ 100 = $14.50

Answer(s): $14.50