Answer:
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
<u> +100=+100</u>
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!
