How to find two numbers by their sum and difference in Excel in 10 seconds

Faced with a classic mathematical problem where you know the sum and difference of two numbers, but don’t know how to quickly calculate it in a table? In this article, xrust and I will analyze a simple mathematical rule, translate it into Excel formulas, and create a universal calculator for instantly solving such problems.

To solve this problem, we first find the numbers themselves mathematically, and then write down the formulas for Excel.

Let the first (larger) number be (x), and the second one be (y).
We have a system of equations:

1. (x + y = 2588)
2. (x — y = 148)

Part 1. Solution in specific numbers

Mathematical calculation:

1. Let's add two equations: ((x + y) + (x — y) = 2588 + 148)
   (2x = 2736)
   (x = 2736/2 = 1368)
2. Substitute (x) into the first equation: (1368 + y = 2588)
   (y = 2588 — 1368 = 1220)

Step-by-step solution in Excel:

1. Open a blank Excel sheet.
2. In cell A1 enter the number 2588 (sum).
3. In cell A2 enter the number 148 (difference).
4. In cell A3 enter the formula to find the first number: =(A1+A2)/2 (result: 1368 ).
5. In cell A4 enter the formula to find the second number: =(A1-A2)/2 or =A1-A3 (result: 1220 ).

Part 2. General solution class=»notranslate»>__GTAG23__

If the sum of two numbers is (S), and their difference is (D), then the system looks like this:

1. (x + y = S)
2. (x — y = D)

Mathematical calculation:

1. Add the equations: (2x = S + D Rightarrow mathbf{x = (S + D)/2})
2. Subtract the second from the first equation: (2y = S — D Rightarrow mathbf{y = (S — D)/2})

Step-by-step solution in Excel for any numbers:

1. In cell A1 sign: Amount (S). In cell B1 you will enter any amount value.
2. In cell A2 sign: Difference (D). In cell B2 you will enter any difference value.
3. In cell A3 sign: First number (x). In cell B3 enter the universal formula:
   =(B1+B2)/2
4. In cell A4 sign: Second number (y). In cell B4 enter the universal formula:
   =(B1-B2)/2

Now, if you change the numbers in cells B1 and B2, Excel will automatically instantly recalculate the result for the new pair of conditions.

Xrust How to find two numbers by their sum and difference in Excel in 10 seconds