Two trains, Train A and Train B, weigh a total of 150 tons. Train A is heavier than train B. The difference of their weights is 100 tons. What is the weight of each train?

train b.

Step-by-step explanation:

becus of the 150 tons and 100 tons

Train A: 125 tons

Train B: 25 tons

Step-by-step explanation:

We can write the situation as a+b=150, and we can also write the value for train b as a-100=b.

To make the equations have only one variable, we can use the substitution method to create a+(a-100)=100. In this, since we know what b equals, we were able to replace the b in the first equation with the value of b in the second equation. Next, we solve the problem for a.

a+(a-100)=150

a+a-100=150

2a-100=150

   +100=+100

2a=250

250/2=125

a=125

Now that we know that train A is 125 tons, we can plug 125 in the equation that represents the weight of train B. Train B is 100 tons lighter than train A, and the equation for train b is a-100=b. We can replace a with 125, creating 125-100=b.

Solve.

125-100=b

25=b

Check answers.

a+b=150

a=125

b=25

125+25=150

150=150

The answers are equal!! So, this means train B is 25 tons, and train A is 125.

Hope this helps!