Reggie Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 80 minutes of talk time for $13.60. Plan B offers 240 SMS and 150 minutes of talk time for $22.20. Reggie Mobile Company is also going to launch Plan C which offers 170 SMS and 250 minutes of talk time. How much should Reggie 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 + 80 min = 1360 --- (1)

Plan B = 240 SMS + 150 min = 2220 --- (2)

Make the cost of SMS the same.

(1)_x8
1200 SMS + 640 min = 10880 --- (3)

(2)_x5
1200 SMS + 750 min = 11100 --- (4)

(4) - (3)
750 min - 640 min = 11100 - 10880
110 min = 220

1 min = 220 ÷ 110 = 2

80 min = 80 x 2 = 160

From (1):
150 SMS + 80 min = 1360 
150 SMS + 80 x 2 = 1360
150 SMS + 160 = 1360
150 SMS = 1360 - 160
150 SMS = 1200

1 SMS = 1200 ÷ 150 = 8

170 SMS
= 170 x 8
= 1360

250 min
= 250 x 2
= 500

Charges for Plan C
= 170 SMS + 250 min
= 1360 + 500
= 1860¢

1860¢ = 1860 ÷ 100 = $18.60

Answer(s): $18.60