Gabriel Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 70 minutes of talk time for $8.10. Plan B offers 180 SMS and 170 minutes of talk time for $14.10. Gabriel Mobile Company is also going to launch Plan C which offers 180 SMS and 210 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 = 120 SMS + 70 min = 810 --- (1)

Plan B = 180 SMS + 170 min = 1410 --- (2)

Make the cost of SMS the same.

(1)_x3
360 SMS + 210 min = 2430 --- (3)

(2)_x2
360 SMS + 340 min = 2820 --- (4)

(4) - (3)
340 min - 210 min = 2820 - 2430
130 min = 390

1 min = 390 ÷ 130 = 3

70 min = 70 x 3 = 210

From (1):
120 SMS + 70 min = 810 
120 SMS + 70 x 3 = 810
120 SMS + 210 = 810
120 SMS = 810 - 210
120 SMS = 600

1 SMS = 600 ÷ 120 = 5

180 SMS
= 180 x 5
= 900

210 min
= 210 x 3
= 630

Charges for Plan C
= 180 SMS + 210 min
= 900 + 630
= 1530¢

1530¢ = 1530 ÷ 100 = $15.30

Answer(s): $15.30