Bobby Mobile Company has a few mobile phone service plans. Plan A offers 160 SMS and 50 minutes of talk time for $13.80. Plan B offers 360 SMS and 190 minutes of talk time for $32.60. Bobby Mobile Company is also going to launch Plan C which offers 160 SMS and 280 minutes of talk time. How much should Bobby 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 = 160 SMS + 50 min = 1380 --- (1)

Plan B = 360 SMS + 190 min = 3260 --- (2)

Make the cost of SMS the same.

(1)_x9
1440 SMS + 450 min = 12420 --- (3)

(2)_x4
1440 SMS + 760 min = 13040 --- (4)

(4) - (3)
760 min - 450 min = 13040 - 12420
310 min = 620

1 min = 620 ÷ 310 = 2

50 min = 50 x 2 = 100

From (1):
160 SMS + 50 min = 1380 
160 SMS + 50 x 2 = 1380
160 SMS + 100 = 1380
160 SMS = 1380 - 100
160 SMS = 1280

1 SMS = 1280 ÷ 160 = 8

160 SMS
= 160 x 8
= 1280

280 min
= 280 x 2
= 560

Charges for Plan C
= 160 SMS + 280 min
= 1280 + 560
= 1840¢

1840¢ = 1840 ÷ 100 = $18.40

Answer(s): $18.40