Question

How do I calculate the prices of two items when I know their sum and difference?

Answer 1

To calculate the prices of two items when you know their sum and difference, you can set up a simple mathematical system using two variables.

Let's denote the prices of the two items as:

- \( x \): Price of the first item
- \( y \): Price of the second item

You will have two equations based on the information about their sum and difference:

1. The sum of the prices:
\( x + y = S \) (where \( S \) is the known sum)

2. The difference of the prices:
\( x - y = D \) (where \( D \) is the known difference)

You can solve these equations step by step:

### Step 1: Write down the equations
You have:
- \( x + y = S \)
- \( x - y = D \)

### Step 2: Solve for \( x \) and \( y \)
To find \( x \), you can add the two equations:
\[
(x + y) + (x - y) = S + D
\]
This simplifies to:
\[
2x = S + D
\]
Now, divide by 2:
\[
x = \frac{S + D}{2}
\]

Next, to find \( y \), you can subtract the second equation from the first equation:
\[
(x + y) - (x - y) = S - D
\]
This simplifies to:
\[
2y = S - D
\]
Now, divide by 2:
\[
y = \frac{S - D}{2}
\]

### Conclusion
Now you have the prices:
- Price of the first item \( x = \frac{S + D}{2} \)
- Price of the second item \( y = \frac{S - D}{2} \)

Just substitute the values of \( S \) (sum) and \( D \) (difference) into these equations to find the prices of the two items.