Fred Mobile Company has a few mobile phone service plans. Plan A offers 200 SMS and 50 minutes of talk time for $19.50. Plan B offers 240 SMS and 100 minutes of talk time for $24.60. Fred Mobile Company is also going to launch Plan C which offers 180 SMS and 290 minutes of talk time. How much should Fred 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 + 50 min = 1950 --- (1)

Plan B = 240 SMS + 100 min = 2460 --- (2)

Make the cost of SMS the same.

(1)_x6
1200 SMS + 300 min = 11700 --- (3)

(2)_x5
1200 SMS + 500 min = 12300 --- (4)

(4) - (3)
500 min - 300 min = 12300 - 11700
200 min = 600

1 min = 600 ÷ 200 = 3

50 min = 50 x 3 = 150

From (1):
200 SMS + 50 min = 1950 
200 SMS + 50 x 3 = 1950
200 SMS + 150 = 1950
200 SMS = 1950 - 150
200 SMS = 1800

1 SMS = 1800 ÷ 200 = 9

180 SMS
= 180 x 9
= 1620

290 min
= 290 x 3
= 870

Charges for Plan C
= 180 SMS + 290 min
= 1620 + 870
= 2490¢

2490¢ = 2490 ÷ 100 = $24.90

Answer(s): $24.90