Tom Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 60 minutes of talk time for $11.70. Plan B offers 350 SMS and 180 minutes of talk time for $28.10. Tom Mobile Company is also going to launch Plan C which offers 140 SMS and 300 minutes of talk time. How much should Tom 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 + 60 min = 1170 --- (1)

Plan B = 350 SMS + 180 min = 2810 --- (2)

Make the cost of SMS the same.

(1)_x7
1050 SMS + 420 min = 8190 --- (3)

(2)_x3
1050 SMS + 540 min = 8430 --- (4)

(4) - (3)
540 min - 420 min = 8430 - 8190
120 min = 240

1 min = 240 ÷ 120 = 2

60 min = 60 x 2 = 120

From (1):
150 SMS + 60 min = 1170 
150 SMS + 60 x 2 = 1170
150 SMS + 120 = 1170
150 SMS = 1170 - 120
150 SMS = 1050

1 SMS = 1050 ÷ 150 = 7

140 SMS
= 140 x 7
= 980

300 min
= 300 x 2
= 600

Charges for Plan C
= 140 SMS + 300 min
= 980 + 600
= 1580¢

1580¢ = 1580 ÷ 100 = $15.80

Answer(s): $15.80