Jack Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 90 minutes of talk time for $21.60. Plan B offers 350 SMS and 160 minutes of talk time for $37.90. Jack Mobile Company is also going to launch Plan C which offers 150 SMS and 230 minutes of talk time. How much should Jack 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 = 200 SMS + 90 min = 2160 --- (1)

Plan B = 350 SMS + 160 min = 3790 --- (2)

Make the cost of SMS the same.

(1)_x7
1400 SMS + 630 min = 15120 --- (3)

(2)_x4
1400 SMS + 640 min = 15160 --- (4)

(4) - (3)
640 min - 630 min = 15160 - 15120
10 min = 40

1 min = 40 ÷ 10 = 4

90 min = 90 x 4 = 360

From (1):
200 SMS + 90 min = 2160 
200 SMS + 90 x 4 = 2160
200 SMS + 360 = 2160
200 SMS = 2160 - 360
200 SMS = 1800

1 SMS = 1800 ÷ 200 = 9

150 SMS
= 150 x 9
= 1350

230 min
= 230 x 4
= 920

Charges for Plan C
= 150 SMS + 230 min
= 1350 + 920
= 2270¢

2270¢ = 2270 ÷ 100 = $22.70

Answer(s): $22.70