Jenson Mobile Company has a few mobile phone service plans. Plan A offers 120 SMS and 50 minutes of talk time for $13.50. Plan B offers 210 SMS and 130 minutes of talk time for $24.90. Jenson Mobile Company is also going to launch Plan C which offers 160 SMS and 270 minutes of talk time. How much should Jenson 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 + 50 min = 1350 --- (1)

Plan B = 210 SMS + 130 min = 2490 --- (2)

Make the cost of SMS the same.

(1)_x7
840 SMS + 350 min = 9450 --- (3)

(2)_x4
840 SMS + 520 min = 9960 --- (4)

(4) - (3)
520 min - 350 min = 9960 - 9450
170 min = 510

1 min = 510 ÷ 170 = 3

50 min = 50 x 3 = 150

From (1):
120 SMS + 50 min = 1350 
120 SMS + 50 x 3 = 1350
120 SMS + 150 = 1350
120 SMS = 1350 - 150
120 SMS = 1200

1 SMS = 1200 ÷ 120 = 10

160 SMS
= 160 x 10
= 1600

270 min
= 270 x 3
= 810

Charges for Plan C
= 160 SMS + 270 min
= 1600 + 810
= 2410¢

2410¢ = 2410 ÷ 100 = $24.10

Answer(s): $24.10