Ashipment of 18 cars, some weighing 3000lb a piece and th eothers 5000lb each, has a total weight of 30 tons. find the number of each kind of car.

There are 15 - 3000lb cars and 3 - 5000lb cars.

Step-by-step explanation:

We can solve a problem with two variables by setting up a system of equations based on the information given in the problem.  

Since we know that there are 18 cars total, our first equation is:

a + b = 15, where a = the amount of 3000lb cars and b = the amount of 5000lb cars.

We also know that the total weight of the cars is 30 tons, or 60,000lbs. So, the second equation is:

3000a + 5000b = 60,000

Using our first equation to solve for 'b', we get b = 15 - a.  We can then substitute this expression in for 'b' in the second equation:

3000a + 5000(18 - a) = 60,000

Distribute and combine like terms: 3000a + 90,000 - 5000a = 60,000 or 90,000 - 2000a = 60,000

Subtract 90,000 from both sides and divide by -2000 gives us a = 15.

15 + b = 18, so b = 3.