Question

Two trains, Train A and Train B, weigh a total of 389 tons. Train A is heavier than Train B. The difference of their weights is 263 tons. What is the weight of each train? Equation 1: ____________ Equation 2: ___________ Train A weight: ________ Train B weight: ________

Answer 1

9514 1404 393

Answer:

• A + B = 389
• A - B = 263
• A = 326 tons
• B = 63 tons

Explanation:

The first equation is an expression of the first given relationship:

A + B = 389 . . . . . . where A and B represents trains weights, respectively

The second equation is an expression of the relationship described in the next two sentences:

A - B = 263

__

These equations can be solved by adding them together:

(A +B) +(A -B) = 389 +263

2A = 652 . . . . . . simplify

A = 326 . . . . . . . .divide by 2*

B = 326 -263 = 63

Train A weighs 326 tons.

Train B weighs 63 tons.

_____

* You may notice that this value is the average of the given sum and difference. That observation is true of all "sum and difference" problems.