Mark Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 70 minutes of talk time for $22.80. Plan B offers 360 SMS and 170 minutes of talk time for $42.80. Mark Mobile Company is also going to launch Plan C which offers 150 SMS and 240 minutes of talk time. How much should Mark 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 + 70 min = 2280 --- (1)

Plan B = 360 SMS + 170 min = 4280 --- (2)

Make the cost of SMS the same.

(1)_x9
1800 SMS + 630 min = 20520 --- (3)

(2)_x5
1800 SMS + 850 min = 21400 --- (4)

(4) - (3)
850 min - 630 min = 21400 - 20520
220 min = 880

1 min = 880 ÷ 220 = 4

70 min = 70 x 4 = 280

From (1):
200 SMS + 70 min = 2280 
200 SMS + 70 x 4 = 2280
200 SMS + 280 = 2280
200 SMS = 2280 - 280
200 SMS = 2000

1 SMS = 2000 ÷ 200 = 10

150 SMS
= 150 x 10
= 1500

240 min
= 240 x 4
= 960

Charges for Plan C
= 150 SMS + 240 min
= 1500 + 960
= 2460¢

2460¢ = 2460 ÷ 100 = $24.60

Answer(s): $24.60