Question

Two​ trains, Train A and Train​ B, weigh a total of 147 tons. Train A is heavier than Train B. The difference of their weights is 65 tons. What is the weight of each​ train?

Answer 1

• A: 106 tons
• B: 41 tons

Explanation:

Given trains A and B have weights that total 147 tons, with train A being heavier by 65 tons, you want the weight of each.

Sum and Difference

The relations given in the problem can be expressed as ...

A + B = 147 . . . . . . the total weight

A - B = 65 . . . . . . . the difference of weights (A is heavier)

Solution

The equations can be added to eliminate the B variable:

(A +B) +(A -B) = (147) +(65)

2A = 212 . . . . simplify

A = 106 . . . . . divide by 2

The other weight can be found any number of ways. One way is to subtract the difference here:

B = A -65 = 106 -65 = 41

Train A weighs 106 tons; train B weighs 41 tons.

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Additional comment

You will see "sum and difference" problems in many forms. The solution is always the same: the greater value is half the sum of the given numbers; the lesser value is half their difference.

A = (147 +65)/2 = 212/2 = 106

B = (147 -65)/2 = 82/2 = 41