Sum and Difference Calculator (Find Two Numbers)

Enter the sum and difference of two numbers and instantly find the larger and smaller number. Includes a bar diagram, step-by-step solution, and a check.

Input

Enter the sum (total) and the difference of two numbers to find the larger and the smaller number.

Sum (total of the two numbers)

Difference (gap between the two numbers)

For the difference, enter only its size, no matter which number is larger.

Result

Larger number

Smaller number

How to solve

Step 1: Remove the difference 20 from the sum 100; what remains is twice the smaller number.

Step 2: Smaller number = (100 - 20) / 2 = 40.

Step 3: Larger number = 40 + 20 = 60.

Verification

Check the sum

60 + 40 = 100

Check the difference

60 - 40 = 20

How it works

This is the classic sum-and-difference word problem: given the sum and the difference of two numbers, find each number.
Using a bar diagram, removing the difference from the sum leaves twice the smaller number.
Smaller number = (sum - difference) / 2.
Larger number = (sum + difference) / 2, or equivalently smaller number plus the difference.
You can verify the answer: adding the two numbers gives the sum, and subtracting them gives the difference.
If the sum and difference do not share the same parity (both even or both odd), the two numbers will not be whole numbers.

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