Justin Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 90 minutes of talk time for $12.60. Plan B offers 180 SMS and 150 minutes of talk time for $19.20. Justin Mobile Company is also going to launch Plan C which offers 150 SMS and 210 minutes of talk time. How much should Justin 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 + 90 min = 1260 --- (1)

Plan B = 180 SMS + 150 min = 1920 --- (2)

Make the cost of SMS the same.

(1)_x3
360 SMS + 270 min = 3780 --- (3)

(2)_x2
360 SMS + 300 min = 3840 --- (4)

(4) - (3)
300 min - 270 min = 3840 - 3780
30 min = 60

1 min = 60 ÷ 30 = 2

90 min = 90 x 2 = 180

From (1):
120 SMS + 90 min = 1260 
120 SMS + 90 x 2 = 1260
120 SMS + 180 = 1260
120 SMS = 1260 - 180
120 SMS = 1080

1 SMS = 1080 ÷ 120 = 9

150 SMS
= 150 x 9
= 1350

210 min
= 210 x 2
= 420

Charges for Plan C
= 150 SMS + 210 min
= 1350 + 420
= 1770¢

1770¢ = 1770 ÷ 100 = $17.70

Answer(s): $17.70