Sean Mobile Company has a few mobile phone service plans. Plan A offers 250 SMS and 50 minutes of talk time for $14.50. Plan B offers 350 SMS and 170 minutes of talk time for $24.30. Sean Mobile Company is also going to launch Plan C which offers 130 SMS and 200 minutes of talk time. How much should Sean 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 = 1450 --- (1)

Plan B = 350 SMS + 170 min = 2430 --- (2)

Make the cost of SMS the same.

(1)_x7
1750 SMS + 350 min = 10150 --- (3)

(2)_x5
1750 SMS + 850 min = 12150 --- (4)

(4) - (3)
850 min - 350 min = 12150 - 10150
500 min = 2000

1 min = 2000 ÷ 500 = 4

50 min = 50 x 4 = 200

From (1):
250 SMS + 50 min = 1450 
250 SMS + 50 x 4 = 1450
250 SMS + 200 = 1450
250 SMS = 1450 - 200
250 SMS = 1250

1 SMS = 1250 ÷ 250 = 5

130 SMS
= 130 x 5
= 650

200 min
= 200 x 4
= 800

Charges for Plan C
= 130 SMS + 200 min
= 650 + 800
= 1450¢

1450¢ = 1450 ÷ 100 = $14.50

Answer(s): $14.50