Lex was chatting with his friends thomas and mike. He was wondering how much it will cost him to take a taxi from his house to work, a total of 12 km. Thomas and mike both recently tok a taxi from the same company that charge a intial fee and also a constant rate per km travelled. Neither can remember how much the rates were but they have the receipt. Thomas traveled 10km and paid %24.50. Mike traveled 15km and paid $35. How much wwill Lex pay to travel a distance of 12km.

$28.3

Step-by-step explanation:

x=rate for 1km

y=initial fee

Mike: $35 for 15km -> 35 = 15x + y

Thomas: $24.50 for 10km -> 24.50 = 10x + y

Using those two equations we see the following:

Mike paid $10.5 more for 5 more km. The initial fee remains unchanged, so we can calculate the rate for 1km, which is 10.5/5=2.1.

35 = 15x + y

24.50 = 10x + y

10.5 = 5x

2.1=x

Using that value with one of the original equations we can calculate the initial fee.

35 = 15x + y

35 = 15*2.1 + y

35 = 31.5 + y

3.5 = y

Mike paid 15*2.1=31.5 ($2.1 for every km) plus the initial fee, his total was $35.

We subtract the 31.5 from the 35(total) and get the initial fee, which is $3.5.

Let's see what Lex will pay:

Km travelled times 2.1 (the rate for 1km) plus 3.5 (the initial fee).

12*2.1 + 3.5 = 28.3

Lex will pay $28.3 for the same taxi company to travel 12 km.