Tom Mobile Company has a few mobile phone service plans. Plan A offers 150 SMS and 50 minutes of talk time for $9.50. Plan B offers 270 SMS and 190 minutes of talk time for $21.10. Tom Mobile Company is also going to launch Plan C which offers 160 SMS and 290 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 + 50 min = 950 --- (1)

Plan B = 270 SMS + 190 min = 2110 --- (2)

Make the cost of SMS the same.

(1)_x9
1350 SMS + 450 min = 8550 --- (3)

(2)_x5
1350 SMS + 950 min = 10550 --- (4)

(4) - (3)
950 min - 450 min = 10550 - 8550
500 min = 2000

1 min = 2000 ÷ 500 = 4

50 min = 50 x 4 = 200

From (1):
150 SMS + 50 min = 950 
150 SMS + 50 x 4 = 950
150 SMS + 200 = 950
150 SMS = 950 - 200
150 SMS = 750

1 SMS = 750 ÷ 150 = 5

160 SMS
= 160 x 5
= 800

290 min
= 290 x 4
= 1160

Charges for Plan C
= 160 SMS + 290 min
= 800 + 1160
= 1960¢

1960¢ = 1960 ÷ 100 = $19.60

Answer(s): $19.60